Physics Book - User contributions [en]

Maxwell's Electromagnetic Theory

2016-11-28T02:27:41Z

Gnewville3:

Written by Megan Sales. Edited by Grace Newville.

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space for many different varying scenarios.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

These are the four complete Maxwell Equations in their integral form.

1) Gauss's Law relates electric field to the charge enclosed by a "Gaussian Surface." The integral represents the sum of electric flux, so by finding this and multiplying by epsilon-zero, the charge enclosed by the surface may be calculated.

2) Gauss's Law for magnetism states that the sum of magnetic flux for a specific area is equal to zero.

3) Faraday's Law directly relates electric and magnetic fields by being able to find the non-Coulomb Electric field that is produced due to a magnetic field and current.

4) Ampere-Maxwell Law is perhaps the most complex of Maxwell's Equations, and involves the derivative of electric flux.

[[File:Maxwell_equation.jpg]]

This is the four complete Maxwell Equations in their differential form.

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios, but the key idea is that a time-varying magnetic field is associated with an electric field and vice versa. This leads to the concept that by solving the partial differential equations given by these four equations, all fields traveling through space may be modeled, but for most cases the calculations are so complex that they must be done computationally.

Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==
I first saw Maxwell's Equations in my thermodynamics class last semester. That is what prompted me to explore the theory behind them, as I had only used them in a practical application. That being said, this [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something I use as a chemical engineer.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2016-11-28T02:18:19Z

Gnewville3: /* A Computational Model */

Written by Megan Sales. '''CLAIMED BY GRACE NEWVILLE FALL 2016'''

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

[[File:Maxwell_equation.jpg]]

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios, but the key idea is that a time-varying magnetic field is associated with an electric field and vice versa. This leads to the concept that by solving the partial differential equations given by these four equations, all fields traveling through space may be modeled, but for most cases the calculations are so complex that they must be done computationally.

Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==
I first saw Maxwell's Equations in my thermodynamics class last semester. That is what prompted me to explore the theory behind them, as I had only used them in a practical application. That being said, this [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something I use as a chemical engineer.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2016-11-28T02:13:24Z

Gnewville3: /* The Main Idea */

Written by Megan Sales. '''CLAIMED BY GRACE NEWVILLE FALL 2016'''

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

[[File:Maxwell_equation.jpg]]

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios. Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==
I first saw Maxwell's Equations in my thermodynamics class last semester. That is what prompted me to explore the theory behind them, as I had only used them in a practical application. That being said, this [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something I use as a chemical engineer.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2016-11-28T02:10:52Z

Gnewville3: /* The Main Idea */

Written by Megan Sales. '''CLAIMED BY GRACE NEWVILLE FALL 2016'''

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space.

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

[[File:Maxwell_equation.jpg]]

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios. Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==
I first saw Maxwell's Equations in my thermodynamics class last semester. That is what prompted me to explore the theory behind them, as I had only used them in a practical application. That being said, this [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something I use as a chemical engineer.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2016-10-31T19:31:10Z

Gnewville3:

Written by Megan Sales. '''CLAIMED BY GRACE NEWVILLE FALL 2016'''

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. The theory is also the source of the heavily used Maxwell Equations.

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

[[File:Maxwell_equation.jpg]]

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios. Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==
I first saw Maxwell's Equations in my thermodynamics class last semester. That is what prompted me to explore the theory behind them, as I had only used them in a practical application. That being said, this [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something I use as a chemical engineer.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

[[Category: Theory]]

System & Surroundings

2016-04-20T03:51:04Z

Gnewville3:

==Introduction: System, Surroundings, and Energy Accounting==
When it comes to energy, choosing what is the system versus what is the surroundings greatly affects what needs to be accounted for when solving for various values. Choosing certain objects to be apart of the system rather than the surroundings can have an extreme effect on the outcome of said variables, especially when the surroundings do a fairly large amount of work on the system. By definition, a system is a specific part of the universe that we choose to study, while the surroundings are everything else that 'surrounds,' and typically has a significant effect on, the system. This page will analyze how different choices of systems can affect the components of the Energy Principle when relating it to the system.

===The Energy Principle===
To first understand the impact of the choice of system, it is best to fully understand the Energy Principle. The Energy Principle is based off of the fact that energy is a conserved quantity, meaning that it cannot be created nor destroyed. This definition of the conservation of energy gives the equation:
''∆Esystem + ∆Esurroundings = 0''
This best shows the idea that since energy is a conserved quantity, systems may only gain/lose energy if the surroundings lose/gain that same amount. This can be pictured in the image below.
[[File:Image33333.png]]
The Energy Principle can then be arranged by using the fact that the change in energy of a specific system is equal to the work done on the system by the surroundings.
''∆Esystem = W''
where ∆Esystem = Ef - Ei, making this equation now equal to:
''Ef = Ei + W''
The above equation will be what will primarily be used when accounting for all energy terms when the choice of system/surroundings changes.

==Choice of System==
Although physical results are always consistent, choosing different objects as the system changes the form of the energy equation that needs to be used, and which energy terms must be included in order to calculate accurate values for unknowns. In the following example, a fairly complex system will be analyzed in several different ways. Each of these will show a different choice of system and surroundings and how this effects the Energy Principle.

[[File:Image7459842.png]]

===Example===
In this example, a man is lifting his child in the air straight above his head as shown in the picture below. Two different choices of system will be analyzed, one in which the man, child, and Earth are all the system and the other where just the child is the system. By analyzing these two scenarios, it will become much clearer how the specific choice of system varies how equations are formed and calculations are carried out.

'''1) Man, Child, and the Earth'''

In this first situation, the system consists of the man, the child, and the Earth, while there is nothing deemed significant enough to include in the surroundings. In the intial state, the child is at rest, while in the final state the child has moved up above the man's head a distance, d, and has a specific velocity, v. Since there is nothing significant in the surroundings, the work is equal to 0. This gives the following equation:
''Ef = Ei + W
Kf + Uf + Eman,f = Ki + Ui + Eman,i +W
Kf + mgd + Eman,f = 0 + 0 + Eman,i + 0
Eman,f - Eman,i = -(Kf + mgd)
∆Eman = -(Kf +mgd)''

The formula for kinetic energy can then be used to solve for the change in energy of the man.

'''2) Child'''

In the second situation, the child is the only object in the system, which means that the man and the Earth are the surroundings. The initial and final conditions are the same as in the previous analysis, so the child still moves a distance upward, d, with velocity, v. The only difference is now that there are significant objects in the surroundings, the term for work is no longer equal to zero since both of these objects have an impact on the object. An equation for this situation can be found below:
''Ef = Ei + W
Kf = Ki + Wman + W earth
Kf = 0 + Fd - mgd
Kf = Fd - mgd''

By analyzing the systems/surroundings in these different ways, different variables can be found by relating the resulting equations to solve for unknowns. This sort of idea applies to many different situations involving energy, and it is very useful and necessary to be able to determine which factors must be included.

==External links==

''Thinking about Physics Thinking'' by Professor Michael Schatz [https://youtu.be/lr_89uaChps?t=1m4s]

==References==

Matter and Interactions 4th Edition

''Thinking about Physics Thinking''

--[[User:Gnewville3|Gnewville3]] ([[User talk:Gnewville3|talk]]) 22:39, 19 April 2016 (EDT)

File:Image7459842.png

2016-04-20T03:45:14Z

Gnewville3:

System & Surroundings

2016-04-20T03:44:40Z

Gnewville3:

==Introduction: System, Surroundings, and Energy Accounting==
When it comes to energy, choosing what is the system versus what is the surroundings greatly affects what needs to be accounted for when solving for various values. Choosing certain objects to be apart of the system rather than the surroundings can have an extreme effect on the outcome of said variables, especially when the surroundings do a fairly large amount of work on the system. By definition, a system is a specific part of the universe that we choose to study, while the surroundings are everything else that 'surrounds,' and typically has a significant effect on, the system. This page will analyze how different choices of systems can affect the components of the Energy Principle when relating it to the system.

===The Energy Principle===
To first understand the impact of the choice of system, it is best to fully understand the Energy Principle. The Energy Principle is based off of the fact that energy is a conserved quantity, meaning that it cannot be created nor destroyed. This definition of the conservation of energy gives the equation:
''∆Esystem + ∆Esurroundings = 0''
This best shows the idea that since energy is a conserved quantity, systems may only gain/lose energy if the surroundings lose/gain that same amount. This can be pictured in the image below.
[[File:Image33333.png]]
The Energy Principle can then be arranged by using the fact that the change in energy of a specific system is equal to the work done on the system by the surroundings.
''∆Esystem = W''
where ∆Esystem = Ef - Ei, making this equation now equal to:
''Ef = Ei + W''
The above equation will be what will primarily be used when accounting for all energy terms when the choice of system/surroundings changes.

==Choice of System==
Although physical results are always consistent, choosing different objects as the system changes the form of the energy equation that needs to be used, and which energy terms must be included in order to calculate accurate values for unknowns. In the following example, a fairly complex system will be analyzed in several different ways. Each of these will show a different choice of system and surroundings and how this effects the Energy Principle.

===Example===
In this example, a man is lifting his child in the air straight above his head as shown in the picture below. Two different choices of system will be analyzed, one in which the man, child, and Earth are all the system and the other where just the child is the system. By analyzing these two scenarios, it will become much clearer how the specific choice of system varies how equations are formed and calculations are carried out.

'''1) Man, Child, and the Earth'''

In this first situation, the system consists of the man, the child, and the Earth, while there is nothing deemed significant enough to include in the surroundings. In the intial state, the child is at rest, while in the final state the child has moved up above the man's head a distance, d, and has a specific velocity, v. Since there is nothing significant in the surroundings, the work is equal to 0. This gives the following equation:
Ef = Ei + W
Kf + Uf + Eman,f = Ki + Ui + Eman,i +W
Kf + mgh + Eman,f = 0 + 0 + Eman,i + 0
Eman,f - Eman,i = -(Kf + mgh)
∆Eman = -(Kf +mgh)

The formula for kinetic energy can then be used to solve for the change in energy of the man.

'''2) Child'''

In the second situation, the child is the only object in the system, which means that the man and the Earth are the surroundings. The initial and final conditions are the same as in the previous analysis, so the child still moves a distance upward, d, with velocity, v. The only difference is now that there are significant objects in the surroundings, the term for work is no longer equal to zero since both of these objects have an impact on the object.

==External links==

''Thinking about Physics Thinking'' by Professor Michael Schatz [https://youtu.be/lr_89uaChps?t=1m4s]

==References==

Matter and Interactions 4th Edition

''Thinking about Physics Thinking''

--[[User:Gnewville3|Gnewville3]] ([[User talk:Gnewville3|talk]]) 22:39, 19 April 2016 (EDT)

System & Surroundings

2016-04-20T03:39:51Z

Gnewville3: /* Example */

==Introduction: System, Surroundings, and Energy Accounting==
When it comes to energy, choosing what is the system versus what is the surroundings greatly affects what needs to be accounted for when solving for various values. Choosing certain objects to be apart of the system rather than the surroundings can have an extreme effect on the outcome of said variables, especially when the surroundings do a fairly large amount of work on the system. By definition, a system is a specific part of the universe that we choose to study, while the surroundings are everything else that 'surrounds,' and typically has a significant effect on, the system. This page will analyze how different choices of systems can affect the components of the Energy Principle when relating it to the system.

===The Energy Principle===
To first understand the impact of the choice of system, it is best to fully understand the Energy Principle. The Energy Principle is based off of the fact that energy is a conserved quantity, meaning that it cannot be created nor destroyed. This definition of the conservation of energy gives the equation:
''∆Esystem + ∆Esurroundings = 0''
This best shows the idea that since energy is a conserved quantity, systems may only gain/lose energy if the surroundings lose/gain that same amount. This can be pictured in the image below.
[[File:Image33333.png]]
The Energy Principle can then be arranged by using the fact that the change in energy of a specific system is equal to the work done on the system by the surroundings.
''∆Esystem = W''
where ∆Esystem = Ef - Ei, making this equation now equal to:
''Ef = Ei + W''
The above equation will be what will primarily be used when accounting for all energy terms when the choice of system/surroundings changes.

==Choice of System==
Although physical results are always consistent, choosing different objects as the system changes the form of the energy equation that needs to be used, and which energy terms must be included in order to calculate accurate values for unknowns. In the following example, a fairly complex system will be analyzed in several different ways. Each of these will show a different choice of system and surroundings and how this effects the Energy Principle.

===Example===
In this example, a man is lifting his child in the air straight above his head as shown in the picture below. Three different choices of system will be analyzed, one in which the man, child, and Earth are all the system, the second in which just the child is the system, and the third in which the child and the Earth is the system. By analyzing these three scenarios, it will become much clearer how the specific choice of system varies how equations are formed and calculations are carried out.

'''1) Man, Child, and the Earth'''

In this first situation, the system consists of the man, the child, and the Earth, while there is nothing deemed significant enough to include in the surroundings. In the intial state, the child is at rest, while in the final state the child has moved up above the man's head a distance, d, and has a specific velocity, v. Since there is nothing significant in the surroundings, the work is equal to 0. This gives the following equation:
Ef = Ei + W
Kf + Uf + Eman,f = Ki + Ui + Eman,i +W
Kf + mgh + Eman,f = 0 + 0 + Eman,f + 0

The formulas for kinetic energy can then be used to solve for the change in energy of the man.

'''2) Child'''

'''3) Child and the Earth'''

==External links==

''Thinking about Physics Thinking'' by Professor Michael Schatz [https://youtu.be/lr_89uaChps?t=1m4s]

==References==

Matter and Interactions 4th Edition

''Thinking about Physics Thinking''

--[[User:Gnewville3|Gnewville3]] ([[User talk:Gnewville3|talk]]) 22:39, 19 April 2016 (EDT)

System & Surroundings

2016-04-20T03:26:32Z

Gnewville3: /* Example */

System & Surroundings

2016-04-20T03:15:26Z

Gnewville3:

File:Image33333.png

2016-04-20T02:42:40Z

Gnewville3:

System & Surroundings

2016-04-20T02:39:02Z

Gnewville3: