Physics Book - User contributions [en]

Producing a Radiative Electric Field

2015-12-08T04:41:31Z

Ck: /* Middling */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

[[File:Acceleration at angle.png]]

If the angle represented by θ is 60 degrees and <math>|a|</math> is 8.1 * 10^14 m/s^2, what is <math>|a_\perp|</math>?

====Procedure====

Because the angle represented by θ is opposite the <math>a_\perp</math> vector, we simply multiply <math>|a|</math> by sin(θ) to compute our answer:

<math> 8.1 * 10^{14} m/s^2 * sin(60) = 7.05 * 10^{14} m/s^2</math>

===Difficult===

[[File:Radiative middling example.png]]
An electron experiences a kick with initial acceleration <math>a_\perp</math>=3.6 * 10^17 in the -z direction at a point (3, 4, -4) away from the origin. Calculate the direction and magnitude of the initial radiative field at the origin and at (2, 3, 0).

====Procedure====
For <math>E_{rad}</math> at the origin,

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{3^2 + 4^2 + 4^2} \approx 6.40</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 6.40} = \frac{8.1 * 10^{7}}{c^2} \approx 9.0 * 10^{-10}</math>

Thus the magnitude of the initial radiative field at the origin is 9.0 * 10^-10 V/m.

For <math>E_{rad}</math> at (2,3,0),

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{1^2 + 1^2 + 4^2} \approx 4.24</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 4.24} = \frac{1.2 * 10^{8}}{c^2} \approx 1.36 * 10^{-9}</math>

Thus the magnitude of the initial radiative field at (2,3,0) is 1.36 * 10^-9 V/m.

As for the directions, because <math>-qa_{\perp}</math> is in the -z direction, both fields also point in the -z direction.

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-08T04:39:51Z

Ck: /* Middling */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

[[File:Acceleration at angle.png]]

If θ is 60 degrees and <math?|a|</math> is 8.1 * 10^14 m/s^2, what is <math>|a_\perp|</math>?

====Procedure====

Because the angle represented by θ is opposite the <math>a_\perp</math> vector, we simply multiply <math>|a|</math> by sin(θ) to compute our answer:

<math> 8.1 * 10^{14} m/s^2 * sin(60) = 7.05 * 10^{14} m/s^2</math>

===Difficult===

[[File:Radiative middling example.png]]
An electron experiences a kick with initial acceleration <math>a_\perp</math>=3.6 * 10^17 in the -z direction at a point (3, 4, -4) away from the origin. Calculate the direction and magnitude of the initial radiative field at the origin and at (2, 3, 0).

====Procedure====
For <math>E_{rad}</math> at the origin,

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{3^2 + 4^2 + 4^2} \approx 6.40</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 6.40} = \frac{8.1 * 10^{7}}{c^2} \approx 9.0 * 10^{-10}</math>

Thus the magnitude of the initial radiative field at the origin is 9.0 * 10^-10 V/m.

For <math>E_{rad}</math> at (2,3,0),

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{1^2 + 1^2 + 4^2} \approx 4.24</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 4.24} = \frac{1.2 * 10^{8}}{c^2} \approx 1.36 * 10^{-9}</math>

Thus the magnitude of the initial radiative field at (2,3,0) is 1.36 * 10^-9 V/m.

As for the directions, because <math>-qa_{\perp}</math> is in the -z direction, both fields also point in the -z direction.

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-08T04:39:07Z

Ck: /* Procedure */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

[[File:Acceleration at angle.png]]

If θ is 60 degrees and <math?|a|</math> is 8.1 * 10^14 m/s^2, what is <math?|a_\perp|</math>?

====Procedure====

Because the angle represented by θ is opposite the <math>a_\perp</math> vector, we simply multiply <math>|a|</math> by sin(θ) to compute our answer:

<math> 8.1 * 10^{14} m/s^2 * sin(60) = 7.05 * 10^{14} m/s^2</math>

===Difficult===

[[File:Radiative middling example.png]]
An electron experiences a kick with initial acceleration <math>a_\perp</math>=3.6 * 10^17 in the -z direction at a point (3, 4, -4) away from the origin. Calculate the direction and magnitude of the initial radiative field at the origin and at (2, 3, 0).

====Procedure====
For <math>E_{rad}</math> at the origin,

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{3^2 + 4^2 + 4^2} \approx 6.40</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 6.40} = \frac{8.1 * 10^{7}}{c^2} \approx 9.0 * 10^{-10}</math>

Thus the magnitude of the initial radiative field at the origin is 9.0 * 10^-10 V/m.

For <math>E_{rad}</math> at (2,3,0),

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{1^2 + 1^2 + 4^2} \approx 4.24</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 4.24} = \frac{1.2 * 10^{8}}{c^2} \approx 1.36 * 10^{-9}</math>

Thus the magnitude of the initial radiative field at (2,3,0) is 1.36 * 10^-9 V/m.

As for the directions, because <math>-qa_{\perp}</math> is in the -z direction, both fields also point in the -z direction.

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-08T04:38:39Z

Ck: /* Procedure */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

[[File:Acceleration at angle.png]]

If θ is 60 degrees and <math?|a|</math> is 8.1 * 10^14 m/s^2, what is <math?|a_\perp|</math>?

====Procedure====

Because the angle represented by θ is opposite the <math?a_\perp</math> vector, we simply multiply <math?|a|</math> by sin(θ) to compute our answer:

<math> 8.1 * 10^{14} m/s^2 * sin(60) = 7.05 * 10^{14} m/s^2</math>

===Difficult===

[[File:Radiative middling example.png]]
An electron experiences a kick with initial acceleration <math>a_\perp</math>=3.6 * 10^17 in the -z direction at a point (3, 4, -4) away from the origin. Calculate the direction and magnitude of the initial radiative field at the origin and at (2, 3, 0).

====Procedure====
For <math>E_{rad}</math> at the origin,

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{3^2 + 4^2 + 4^2} \approx 6.40</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 6.40} = \frac{8.1 * 10^{7}}{c^2} \approx 9.0 * 10^{-10}</math>

Thus the magnitude of the initial radiative field at the origin is 9.0 * 10^-10 V/m.

For <math>E_{rad}</math> at (2,3,0),

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{1^2 + 1^2 + 4^2} \approx 4.24</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 4.24} = \frac{1.2 * 10^{8}}{c^2} \approx 1.36 * 10^{-9}</math>

Thus the magnitude of the initial radiative field at (2,3,0) is 1.36 * 10^-9 V/m.

As for the directions, because <math>-qa_{\perp}</math> is in the -z direction, both fields also point in the -z direction.

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-08T04:38:16Z

Ck:

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

[[File:Acceleration at angle.png]]

If θ is 60 degrees and <math?|a|</math> is 8.1 * 10^14 m/s^2, what is <math?|a_\perp|</math>?

====Procedure====

Because the angle represented by θ is opposite the <math?a_\perp</math> vector, we simply multiply <math?|a|</math> by sin(θ) to compute our answer:

<math> 8.1 * 10^{14} m/s^2 * sin(60) = 7.05 * 10^{14}</math>

===Difficult===

[[File:Radiative middling example.png]]
An electron experiences a kick with initial acceleration <math>a_\perp</math>=3.6 * 10^17 in the -z direction at a point (3, 4, -4) away from the origin. Calculate the direction and magnitude of the initial radiative field at the origin and at (2, 3, 0).

====Procedure====
For <math>E_{rad}</math> at the origin,

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{3^2 + 4^2 + 4^2} \approx 6.40</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 6.40} = \frac{8.1 * 10^{7}}{c^2} \approx 9.0 * 10^{-10}</math>

Thus the magnitude of the initial radiative field at the origin is 9.0 * 10^-10 V/m.

For <math>E_{rad}</math> at (2,3,0),

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{1^2 + 1^2 + 4^2} \approx 4.24</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 4.24} = \frac{1.2 * 10^{8}}{c^2} \approx 1.36 * 10^{-9}</math>

Thus the magnitude of the initial radiative field at (2,3,0) is 1.36 * 10^-9 V/m.

As for the directions, because <math>-qa_{\perp}</math> is in the -z direction, both fields also point in the -z direction.

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

File:Acceleration at angle.png

2015-12-08T04:32:45Z

Ck:

Producing a Radiative Electric Field

2015-12-08T04:32:08Z

Ck: /* Examples */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

===Difficult===

[[File:Radiative middling example.png]]
An electron experiences a kick with initial acceleration <math>a_\perp</math>=3.6 * 10^17 in the -z direction at a point (3, 4, -4) away from the origin. Calculate the direction and magnitude of the initial radiative field at the origin and at (2, 3, 0).

====Procedure====
For <math>E_{rad}</math> at the origin,

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{3^2 + 4^2 + 4^2} \approx 6.40</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 6.40} = \frac{8.1 * 10^{7}}{c^2} \approx 9.0 * 10^{-10}</math>

Thus the magnitude of the initial radiative field at the origin is 9.0 * 10^-10 V/m.

For <math>E_{rad}</math> at (2,3,0),

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{1^2 + 1^2 + 4^2} \approx 4.24</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 4.24} = \frac{1.2 * 10^{8}}{c^2} \approx 1.36 * 10^{-9}</math>

Thus the magnitude of the initial radiative field at (2,3,0) is 1.36 * 10^-9 V/m.

As for the directions, because <math>-qa_{\perp}</math> is in the -z direction, both fields also point in the -z direction.

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-08T03:40:02Z

Ck: /* Middling */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

[[File:Radiative middling example.png]]
An electron experiences a kick with initial acceleration <math>a_\perp</math>=3.6 * 10^17 in the -z direction at a point (3, 4, -4) away from the origin. Calculate the direction and magnitude of the initial radiative field at the origin and at (2, 3, 0).

====Procedure====
For <math>E_{rad}</math> at the origin,

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{3^2 + 4^2 + 4^2} \approx 6.40</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 6.40} = \frac{8.1 * 10^{7}}{c^2} \approx 9.0 * 10^{-10}</math>

Thus the magnitude of the initial radiative field at the origin is 9.0 * 10^-10 V/m.

For <math>E_{rad}</math> at (2,3,0),

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{1^2 + 1^2 + 4^2} \approx 4.24</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 4.24} = \frac{1.2 * 10^{8}}{c^2} \approx 1.36 * 10^{-9}</math>

Thus the magnitude of the initial radiative field at (2,3,0) is 1.36 * 10^-9 V/m.

As for the directions, because <math>-qa_{\perp}</math> is in the -z direction, both fields also point in the -z direction.

===Difficult===

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-08T03:39:47Z

Ck: /* Middling */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

==Middling==

[[File:Radiative middling example.png]]
An electron experiences a kick with initial acceleration <math>a_\perp</math>=3.6 * 10^17 in the -z direction at a point (3, 4, -4) away from the origin. Calculate the direction and magnitude of the initial radiative field at the origin and at (2, 3, 0).

====Procedure====
For <math>E_{rad}</math> at the origin,

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{3^2 + 4^2 + 4^2} \approx 6.40</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 6.40} = \frac{8.1 * 10^{7}}{c^2} \approx 9.0 * 10^{-10}</math>

Thus the magnitude of the initial radiative field at the origin is 9.0 * 10^-10 V/m.

For <math>E_{rad}</math> at (2,3,0),

<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}_\perp}{c^2r}</math>

<math>r=\sqrt{1^2 + 1^2 + 4^2} \approx 4.24</math>

<math>E_{rad}=9 * 10^9\frac{e(3.6 * 10^{17})}{c^2 * 4.24} = \frac{1.2 * 10^{8}}{c^2} \approx 1.36 * 10^{-9}</math>

Thus the magnitude of the initial radiative field at (2,3,0) is 1.36 * 10^-9 V/m.

As for the directions, because <math>-qa_{\perp}</math> is in the -z direction, both fields also point in the -z direction.

===Difficult===

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-08T03:05:53Z

Ck: /* Middling */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

[[File:Radiative middling example.png]]
An electron experiences a kick with initial acceleration <math>a=3.6 * 10^32</math> in the -z direction at a point (3, 4, -4) away from the origin. Calculate the direction and magnitude of the initial radiative field at (2, 3, 0) and the electric field at (1, 1, 0). Then draw these arrows on the graph.

====Procedure====
<math>E_{rad}=\frac{1}{4\pi\epsilon_0}\frac{-q\vec{a}}{c^2r}</math>

===Difficult===

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

File:Radiative middling example.png

2015-12-08T01:30:58Z

Ck: Ck uploaded a new version of "File:Radiative middling example.png"

Producing a Radiative Electric Field

2015-12-08T01:28:08Z

Ck:

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

[[File:Radiative middling example.png]]
An electron experiences a kick in the -z direction at a 3 meters to the right of and 4 meters above the origin. Draw an arrow representing the direction and magnitude of the electric field at (2, 3, 0) and another representing the direction and magnitude of the electric field at (1, 1, 0).

===Difficult===

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

File:Radiative middling example.png

2015-12-08T01:27:58Z

Ck: Ck uploaded a new version of "File:Radiative middling example.png"

File:Radiative middling example.png

2015-12-08T01:25:21Z

Ck:

Producing a Radiative Electric Field

2015-12-08T01:24:31Z

Ck: /* Middling */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===

An electron experiences a kick in the -z direction at a 3 meters to the right of and 4 meters above the origin. Draw an arrow representing the direction and magnitude of the electric field at (2, 3, 0) and another representing the direction and magnitude of the electric field at (1, 1, 0).

===Difficult===

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-07T23:32:12Z

Ck: /* Connectedness */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

'''3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-07T23:31:56Z

Ck: /* Connectedness */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
'''1. How is this topic connected to something that you are interested in?'''

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

'''2. How is it connected to your major?'''

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.
'''
3. Is there an interesting industrial application?'''

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-07T23:31:30Z

Ck:

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>\vec{E}</math> and <math>\vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>\vec{E}</math> and <math>\vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>\vec{E}</math> and <math>\vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-07T23:29:55Z

Ck: /* See also */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

*[[Sinusoidal Electromagnetic Radiaton]]
*[[Electromagnetic Propagation]]
*[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-07T23:29:24Z

Ck: /* References */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information about the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-07T23:29:11Z

Ck: /* References */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html Information about the formulation and calculation of properties of a radiative electric field.
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up Historical information surrounding the physicists who discovered the different types and applications of electromagnetic waves.

Producing a Radiative Electric Field

2015-12-07T23:27:19Z

Ck: /* References */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

*https://www.webassign.net/ebooks/mi4/toc.html
*http://www.jstor.org/stable/info/107057
*https://archive.org/stream/growthofphysical029068mbp#page/n11/mode/2up

Producing a Radiative Electric Field

2015-12-07T23:22:51Z

Ck: /* History */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

2015-12-07T23:22:24Z

Ck: /* External links */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

* [https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/introduction-to-light Introduction to light and electromagnetic radiation]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

2015-12-07T23:20:59Z

Ck: /* Further reading */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Chabay, Ruth W.; Sherwood, Bruce A.(2014). Matter and Interactions (4th ed.). John Wiley & Sons Inc. ISBN 978-1-118-87586-5.
*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

2015-12-07T23:16:13Z

Ck: /* Further reading */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7.
*Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
*Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 0-201-52624-7.
*Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 0-471-30932-X.

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

2015-12-07T23:15:19Z

Ck: /* Further reading */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

*{{cite book
| last = Serway | first = Raymond A.
|author2=Jewett, John W.
| title = Physics for Scientists and Engineers
| edition = 6th
| publisher = Brooks Cole
| year = 2004
| isbn = 0-534-40842-7
}}
*{{cite book
| last = Tipler | first = Paul
| title = Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics
| edition = 5th
| publisher = W. H. Freeman
| year = 2004
| isbn = 0-7167-0810-8
}}
*{{cite book
| last = Reitz | first = John |author2=Milford, Frederick |author3=Christy, Robert
| title = Foundations of Electromagnetic Theory
| edition = 4th
| publisher = Addison Wesley
| year = 1992
| isbn = 0-201-52624-7
}}
*{{cite book
| last = Jackson | first = John David
| authorlink = John David Jackson (physicist)
| title = Classical Electrodynamics
| edition = 3rd
| publisher = John Wiley & Sons
| year = 1999
| isbn = 0-471-30932-X
}}

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

2015-12-07T23:14:52Z

Ck: /* Further reading */

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

{{cite book
| last = Serway | first = Raymond A.
|author2=Jewett, John W.
| title = Physics for Scientists and Engineers
| edition = 6th
| publisher = Brooks Cole
| year = 2004
| isbn = 0-534-40842-7
}}
{{cite book
| last = Tipler | first = Paul
| title = Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics
| edition = 5th
| publisher = W. H. Freeman
| year = 2004
| isbn = 0-7167-0810-8
}}
{{cite book
| last = Reitz | first = John |author2=Milford, Frederick |author3=Christy, Robert
| title = Foundations of Electromagnetic Theory
| edition = 4th
| publisher = Addison Wesley
| year = 1992
| isbn = 0-201-52624-7
}}
{{cite book
| last = Jackson | first = John David
| authorlink = John David Jackson (physicist)
| title = Classical Electrodynamics
| edition = 3rd
| publisher = John Wiley & Sons
| year = 1999
| isbn = 0-471-30932-X
}}

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

2015-12-07T23:14:28Z

Ck:

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

[[Sinusoidal Electromagnetic Radiaton]]
[[Electromagnetic Propagation]]
[[Energy and Momentum Analysis in Radiation]]

===Further reading===

* {{cite book
| last = Serway | first = Raymond A.
|author2=Jewett, John W.
| title = Physics for Scientists and Engineers
| edition = 6th
| publisher = Brooks Cole
| year = 2004
| isbn = 0-534-40842-7
}}
* {{cite book
| last = Tipler | first = Paul
| title = Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics
| edition = 5th
| publisher = W. H. Freeman
| year = 2004
| isbn = 0-7167-0810-8
}}
* {{cite book
| last = Reitz | first = John |author2=Milford, Frederick |author3=Christy, Robert
| title = Foundations of Electromagnetic Theory
| edition = 4th
| publisher = Addison Wesley
| year = 1992
| isbn = 0-201-52624-7
}}
* {{cite book
| last = Jackson | first = John David
| authorlink = John David Jackson (physicist)
| title = Classical Electrodynamics
| edition = 3rd
| publisher = John Wiley & Sons
| year = 1999
| isbn = 0-471-30932-X
}}

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

2015-12-07T23:12:40Z

Ck:

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

2. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

3. Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

* {{cite book
| last = Serway | first = Raymond A.
|author2=Jewett, John W.
| title = Physics for Scientists and Engineers
| edition = 6th
| publisher = Brooks Cole
| year = 2004
| isbn = 0-534-40842-7
}}
* {{cite book
| last = Tipler | first = Paul
| title = Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics
| edition = 5th
| publisher = W. H. Freeman
| year = 2004
| isbn = 0-7167-0810-8
}}
* {{cite book
| last = Reitz | first = John |author2=Milford, Frederick |author3=Christy, Robert
| title = Foundations of Electromagnetic Theory
| edition = 4th
| publisher = Addison Wesley
| year = 1992
| isbn = 0-201-52624-7
}}
* {{cite book
| last = Jackson | first = John David
| authorlink = John David Jackson (physicist)
| title = Classical Electrodynamics
| edition = 3rd
| publisher = John Wiley & Sons
| year = 1999
| isbn = 0-471-30932-X
}}

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

2015-12-07T23:11:53Z

Ck:

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

Is there an interesting industrial application?

Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

* {{cite book
| last = Serway | first = Raymond A.
|author2=Jewett, John W.
| title = Physics for Scientists and Engineers
| edition = 6th
| publisher = Brooks Cole
| year = 2004
| isbn = 0-534-40842-7
}}
* {{cite book
| last = Tipler | first = Paul
| title = Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics
| edition = 5th
| publisher = W. H. Freeman
| year = 2004
| isbn = 0-7167-0810-8
}}
* {{cite book
| last = Reitz | first = John |author2=Milford, Frederick |author3=Christy, Robert
| title = Foundations of Electromagnetic Theory
| edition = 4th
| publisher = Addison Wesley
| year = 1992
| isbn = 0-201-52624-7
}}
* {{cite book
| last = Jackson | first = John David
| authorlink = John David Jackson (physicist)
| title = Classical Electrodynamics
| edition = 3rd
| publisher = John Wiley & Sons
| year = 1999
| isbn = 0-471-30932-X
}}

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

2015-12-07T23:11:25Z

Ck:

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==Calculating Radiative Electric Field==

Maintained by Charles Kilpatrick --[[User:Ck|Ck]] ([[User talk:Ck|talk]]) 14:18, 18 November 2015 (EST)

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge of the accelerated particle, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.

[https://trinket.io/glowscript/ee59ac4ec0 3d Radiation vPython Model]

The acceleration vector, an initial kick in the +x direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent <math>\vec{E}_{radiative}</math> and the cyan arrows represent the corresponding <math>\vec{B}_{radiative}</math> at distance '''r''' from the particle.

==Examples==

===Simple===
An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the +y direction.

===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative <math>vec{E}</math> and <math>vec{B}</math> fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

#How is it connected to your major?
As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over <math>k</math>, all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the <math>vec{E}</math> and <math>vec{B}</math> fields may change and distort upon interacting with other fields as they extend outward.

#Is there an interesting industrial application?
Most practical accelerations of charge will occur on objects with both positive and negative charges. When dipoles are accelerated on more than one axis at once, they produce a cyclical difference in <math>vec{E}</math> and <math>vec{B}</math> fields, resulting in electromagnetic waves, which are used in countless places: radio, microwave ovens, tv remotes, any electronic display... The list goes on.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

While electromagnetic radiation had been found as a phenomenon that produced visible light in the early 1800's, it was not until the 1860's that James Clerk Maxwell was the first to create formal equations to measure electromagnetic field while lecturing at King's College, London. Upon doing so, he found that the speed of propagation of an electric field was approximately the speed of light and later concluded that light itself was a change in electromagnetic field. In 1887, Heinrich Hertz accelerated charges with low frequency in order to produce radio waves while testing Maxwell's equations at the University of Karlsruhe in Germany, and Wilhelm Röntgen in 1895 attached electrodes to a Ruhmkorff coil in to generate an electrostatic charge and eventually discovered X-ray radiation when he noted a flickering produced on a barium platinocyanide screen at the University of Würzburg, Germany. Finally, in 1898, Marie Curie discovered the properties of the elements Polonium and Radium that generate alpha particle radiation through the energetically-excited nuclear state (and thus disruption in charge velocity) of the isotopes at the School of Physics and Chemistry, Paris.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

* {{cite book
| last = Serway | first = Raymond A.
|author2=Jewett, John W.
| title = Physics for Scientists and Engineers
| edition = 6th
| publisher = Brooks Cole
| year = 2004
| isbn = 0-534-40842-7
}}
* {{cite book
| last = Tipler | first = Paul
| title = Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics
| edition = 5th
| publisher = W. H. Freeman
| year = 2004
| isbn = 0-7167-0810-8
}}
* {{cite book
| last = Reitz | first = John |author2=Milford, Frederick |author3=Christy, Robert
| title = Foundations of Electromagnetic Theory
| edition = 4th
| publisher = Addison Wesley
| year = 1992
| isbn = 0-201-52624-7
}}
* {{cite book
| last = Jackson | first = John David
| authorlink = John David Jackson (physicist)
| title = Classical Electrodynamics
| edition = 3rd
| publisher = John Wiley & Sons
| year = 1999
| isbn = 0-471-30932-X
}}

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Ck: /* Calculating Radiative Electric Field */

Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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User:Ck

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ckilpatrick6@gatech.edu

Producing a Radiative Electric Field

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Producing a Radiative Electric Field

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Ck: Created page with "This page explains the relationship between measured radiative electric field and the properties of charges in a system. ==The Main Idea== Calculating Radiative Electric Fie..."

This page explains the relationship between measured radiative electric field and the properties of charges in a system.

==The Main Idea==

Calculating Radiative Electric Field

===A Mathematical Model===

The radiative electric field can be generally modeled as <math>\vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r}</math> where '''q''' is the charge, <math>\vec{a}_\perp</math> is the projected acceleration, '''c''' is the speed of light and '''r''' is the distance between the charge and the observation location.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Main Page

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__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Catagories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Michael Faraday]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Marie Curie]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* Predicting Change in one dimension
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Curving Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Rotation]]
* [[Torque]]
* [[Right Hand Rule]]
* Predicting a Change in Rotation
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
**[[Sign of Potential Difference]]
*[[Electric Force]]
*[[Polarization]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
*[[Ohm's Law]]
*[[RC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Faraday's Law]]
**[[Inductance]]
*[[Ampere-Maxwell Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===VPython guide===
<div class="mw-collapsible-content">
*[[VPython basics]]
</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* An overview of [[VPython]]