Physics Book - User contributions [en]

Potential Difference in a Uniform Field

2017-04-10T00:15:03Z

Emilypark:

By: dachtani3

Claimed by SeongEun Park April, 2017

Electric potential is a scalar quantity that is used to describe the change in electric potential energy per unit charge. This page will elaborate on the change in electric potential in a uniform field.

==The Main Idea==

Potential difference is the change in electric potential between a final and initial location when work is done on a charge to to affect its potential energy. The unit for electric potential is a volt (which is also joule/coulomb). Approximation of uniform field is useful for simple calculation.
It is important to remember that since energy is stored in a form of electric field, there will be no potential energy for a single point charge alone; potential energy, thus the potential difference, exists only when there are pairs of interacting particles.

===A Mathematical Model===

This equation represents potential difference, where V is electric potential, U is electric potential energy, and q is unit charge.
The unit for electric potential is 'V' (volt), where it takes 1 Joules of work to move 1 Coulomb of unit charge per 1 volt.
:<math>\Delta V</math> = <math>\frac{dU}{q} </math>

You can rearrange this equation to also show that electric potential energy is electric potential times unit charge.
:<math>\Delta U</math> = <math>q \Delta V</math>

In addition, you can express electric potential as the sum of the dot product of electric field and displacement in each dimension. This expression is as follows:
:<math>\Delta V</math> = -<math>\vec{E}</math>●<math>\Delta \vec{l}</math> = -(<math>E_{x}</math>●<math>\Delta x</math> + <math>E_{y}</math>●<math>\Delta y</math> + <math>E_{z}</math>●<math>\Delta z</math>)
You can also use dot product notation:
:<math>\Delta V</math> = -<math>\vec{E}</math>●<math>\Delta \vec{l}</math> = <math> (E_{x},E_{y},E_{z})●(dX, dY, dZ) </math>

Potential difference can be either positive or negative because each component of electric field and displacement can be positive or negative. Within this expression, you can also note that the units for the electric field are V/m. We originally learned that units for electric field are N/c, but V/m is also an appropriate unit.

===A Computational Model===

This video showcases 3D-models of the interaction of charges with electric potential and electric potential energy. This video is especially helpful if you want to learn these topics conceptually.

https://www.youtube.com/watch?v=-Rb9guSEeVE

In addition, this image showcases the relationship between electric fields and electric potential. If you take the negative gradient of electric potential, the result is the electric field. The gradient is the direction of the hills seen in the graph representing electric potential.

[[File:3-d_model.jpg]]

==Examples==

===Simple===

Questions 1 and 2 are based on the following situation:

A path consists of two locations. Location 1 is at <0.1,0,0>m and Location 2 is at <0.5,0,0>m. A uniform electric field of <300,0,0> N/C exists in this region pointing from Location 1 to Location 2.

Question 1: What is the difference in electric potential between the two points?

:<math>\Delta{L}</math> = final location - initial location = <0.5, 0,0 > - <0.1, 0, 0> = <0.4, 0, 0> m
:<math>\Delta{V}</math> = -<math>\vec{E}</math>●<math>\Delta \vec{l}</math> = -(<math>E_{x}</math>●<math>\Delta x</math> + <math>E_{y}</math>●<math>\Delta y</math> + <math>E_{z}</math>●<math>\Delta z</math>)
= -(300 N/C*.4 + 0*0 + 0*0)
= -120

Answer: -120 V

Question 2: What is the change in electric potential energy for a proton on this path?

:dU = dV*q = -120 V * 1.6e-19 C = -1.92e-17 J

Answer: - 1.92e-17 J

===Middling===
figure 1:
[[File:Slide1.jpg]]

Key Point to remember about signs:

1) If the path is going in the direction of the electric field, electric potential is decreasing.

:Ex: Refer to Simple Example
:Ex 2: Figure 1
- Consider the path going from point A to point B. The path is in the same direction as the electric field (red arrow).
Because ΔV = -E●Δl = -E●Δr(A->B) = -E●d. This then refers ΔV = Vb-Va < 0, meaning that the electric potential is decreasing.

2) If the path is going in the opposite direction of the electric field, electric potential is increasing.

:Question: Location 1 is at <.1,0,0> and Location 2 is at <.5,0,0>. The uniform electric field is <300,0,0> N/C. The charge travels from Location 2 to Location 1.

:new dl = <.1,0,0> - <.5,0,0> = <-.4,0,0>m
:dV = -Exdx = -(-.4*300) = +120V

:Answer: + 120 V

:Ex 2: Figure 1
- Refer back to the figure 1 above. If the path from point C to D was taken, it is going in the opposite direction of the electric field, which means that ΔV > 0;
therefore, the potential is increasing.

3) If the path is perpendicular to the electric field, electric potential does not change.

:Question: Location 1 is at <.1,0,0> and Location 2 is at <.5,0,0>. The uniform electric field is <0,300,0> N/C. The charge travels from Location 1 to Location 2.

:new dL = <.5,0,0> - <.1,0,0> = <.4,0,0>m
:dV = -(Exdx + Eydy + Exdz) = -(.4*0 + 0*300 +0*0) = 0 V

:Answer: 0V

:Ex 2: Figure 1
- Refer back to the figure 1 above. If the path is going from point B to C, or (point A to D), these points are perpendicular to the electric field. Because no work is required to move a
a charge between them, all points that are perpendicular to same electric field share same electric potential.

===Difficult===

The difficult example will refer to using a path that is not directly parallel to the electric field.

Question: Assume an electric field that has a magnitude of 300 N/C. The electric field is uniform. The path chosen is 5 m, 50 degrees away from the field. What is the difference in electric potential in this situation?

:dV = -E*dl = -E*l*cos(theta)
:dV = -(300 N/C)*(5 m)*cos(50) = -964 V

Answer: -964 V

==Connectedness==

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

:Potential difference is extremely applicable and interesting to me because I am a computer engineer and as a computer engineer, I deal with many things regarding electricity. I am particularly interested in building electric guitar pedals. In addition to the digital signal processing and programming aspect of guitar pedals, there is a lot of physics involved with how they work. Potential difference and electric potential kick in because in addition to the signals that are transmitted throughout the TRS cables, current also runs through them. Obviously, energy and charge are also very prominent in this so they are directly applied to the construction of guitar pedals.

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

:As a computer engineer, in class and ideally in my job after college, I will be dealing with electronics and electricity in action. I am constantly dealing with breadboards, semiconductors, microprocessors, cables, etc. All of these things essentially require a basic understanding of physics topics especially related to electromagnetism.

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

:An interested industrial application of electric potential is the ability to use electric potential sensors in human body electrophysiology. In a study conducted by the Center for Physical Electronics and Quantum Technology, the team utilized these sensors to detect electric signals in the human body. The sensors were mainly built with electrometer amplifiers. Specific to electric potential, the senors focus on displacement current rather than electric current at certain locations. The following signals were detected: electrocardiograms, electroencephalograms, and electro-oculograms, and the sensors were able to find the three signals without directly touching the human body. With these findings, the scientists are able to create "spatio-temporal array imaging" of different areas of the human body, including the heart and brain!

==History==

-Alessandro Volta, and Italian physicist, contributed many ideas and inventions to the field of electricity. He invented the first electric battery, the first electromotive series, and most notably, contributed to the idea of electric potential and its unit, the volt.

-In 1745, Volta was born. He spent most of his childhood experimenting with electricity in his friend's physics lab. When he was 18, he started communicating with physicists, Jean-Antonie Nollet and Giambatista Beccaria, who encouraged him to continue with his experiments.

-In 1775, Volta began teaching physics. He soon was able to isolate methane gas, which he discovered could produce electric sparks. In 1776, Volta put the two ideas together to conclude that he could send electric signals across Italy with the sparking machine.

-In 1778, Volta discovered electric potential, or voltage. He realized that the electric potential in a capacitor is directly proportional to the electric charge in that capacitor.

-In 1800, Volta combined all of his findings to create the voltaic pile, or the first electrochemical cell. This battery made of zinc and copper was able to produce a steady and constant electric current.

-Batteries today serve as the major practical application of electric potential. The unit for electric potential, the Volt, is named after Alessandro Volta and his contributions to the field of electricity.

== See also ==

===Further reading===

'''Books, Articles or other print media on this topic'''

-Electric Potential Difference across a cell membrane:
:https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=electric+potential+difference+journal+articles

-Electric Potential Difference between ion phases:
:http://pubs.acs.org/doi/abs/10.1021/j150300a003

===External links===

'''Internet resources on this topic'''

This video that walks through examples on potential difference in a uniform field:
:https://www.youtube.com/watch?v=mF3VAjcjvOA

This video further discusses electric potential and its concepts:
:https://www.youtube.com/watch?v=wT9AsY79f1k

This video on electric potential energy gives a good background on solving problems before learning specifically about electric potential:
:https://www.khanacademy.org/science/physics/electric-charge-electric-force-and-voltage/electric-potential-voltage/v/electric-potential-energy

==References==

-http://study.com/academy/lesson/what-is-electric-potential-definition-formula-quiz.html

-http://www.famousscientists.org/alessandro-volta/

-http://www.isipt.org/world-congress/3/269.html

-http://maxwell.ucdavis.edu/~electro/potential/overview.html

-Matter & Interactions Vol II: Electric and Magnetic Interactions textbook

[[Category:Fields]]

Potential Difference in a Uniform Field

2017-04-10T00:04:29Z

Emilypark:

By: dachtani3

'''CLAIMED BY SHAN SUEN (FALL 2016) (edited main idea, revised mathematical model, added more reference links, edited some connectedness)'''
Claimed by SeongEun Park April, 2017

Electric potential is a scalar quantity that is used to describe the change in electric potential energy per unit charge. This page will elaborate on the change in electric potential in a uniform field.

==The Main Idea==

Potential difference is the change in electric potential between a final and initial location when work is done on a charge to to affect its potential energy. The unit for electric potential is a volt (which is also joule/coulomb). Approximation of uniform field is useful for simple calculation.

===A Mathematical Model===

This equation represents potential difference, where V is electric potential, U is electric potential energy, and q is unit charge.
The unit for electric potential is 'V' (volt), where it takes 1 Joules of work to move 1 Coulomb of unit charge per 1 volt.
:<math>\Delta V</math> = <math>\frac{dU}{q} </math>

You can rearrange this equation to also show that electric potential energy is electric potential times unit charge.
:<math>\Delta U</math> = <math>q \Delta V</math>

In addition, you can express electric potential as the sum of the dot product of electric field and displacement in each dimension. This expression is as follows:
:<math>\Delta V</math> = -<math>\vec{E}</math>●<math>\Delta \vec{l}</math> = -(<math>E_{x}</math>●<math>\Delta x</math> + <math>E_{y}</math>●<math>\Delta y</math> + <math>E_{z}</math>●<math>\Delta z</math>)
You can also use dot product notation:
:<math>\Delta V</math> = -<math>\vec{E}</math>●<math>\Delta \vec{l}</math> = <math> (E_{x},E_{y},E_{z})●(dX, dY, dZ) </math>

Potential difference can be either positive or negative because each component of electric field and displacement can be positive or negative. Within this expression, you can also note that the units for the electric field are V/m. We originally learned that units for electric field are N/c, but V/m is also an appropriate unit.

===A Computational Model===

This video showcases 3D-models of the interaction of charges with electric potential and electric potential energy. This video is especially helpful if you want to learn these topics conceptually.

https://www.youtube.com/watch?v=-Rb9guSEeVE

In addition, this image showcases the relationship between electric fields and electric potential. If you take the negative gradient of electric potential, the result is the electric field. The gradient is the direction of the hills seen in the graph representing electric potential.

[[File:3-d_model.jpg]]

==Examples==

===Simple===

Questions 1 and 2 are based on the following situation:

A path consists of two locations. Location 1 is at <0.1,0,0>m and Location 2 is at <0.5,0,0>m. A uniform electric field of <300,0,0> N/C exists in this region pointing from Location 1 to Location 2.

Question 1: What is the difference in electric potential between the two points?

:<math>\Delta{L}</math> = final location - initial location = <0.5, 0,0 > - <0.1, 0, 0> = <0.4, 0, 0> m
:<math>\Delta{V}</math> = -<math>\vec{E}</math>●<math>\Delta \vec{l}</math> = -(<math>E_{x}</math>●<math>\Delta x</math> + <math>E_{y}</math>●<math>\Delta y</math> + <math>E_{z}</math>●<math>\Delta z</math>)
= -(300 N/C*.4 + 0*0 + 0*0)
= -120

Answer: -120 V

Question 2: What is the change in electric potential energy for a proton on this path?

:dU = dV*q = -120 V * 1.6e-19 C = -1.92e-17 J

Answer: - 1.92e-17 J

===Middling===
figure 1:
[[File:Slide1.jpg]]

Key Point to remember about signs:

1) If the path is going in the direction of the electric field, electric potential is decreasing.

:Ex: Refer to Simple Example
:Ex 2: Figure 1
- Consider the path going from point A to point B. The path is in the same direction as the electric field (red arrow).
Because ΔV = -E●Δl = -E●Δr(A->B) = -E●d. This then refers ΔV = Vb-Va < 0, meaning that the electric potential is decreasing.

2) If the path is going in the opposite direction of the electric field, electric potential is increasing.

:Question: Location 1 is at <.1,0,0> and Location 2 is at <.5,0,0>. The uniform electric field is <300,0,0> N/C. The charge travels from Location 2 to Location 1.

:new dl = <.1,0,0> - <.5,0,0> = <-.4,0,0>m
:dV = -Exdx = -(-.4*300) = +120V

:Answer: + 120 V

:Ex 2: Figure 1
- Refer back to the figure 1 above. If the path from point C to D was taken, it is going in the opposite direction of the electric field, which means that ΔV > 0;
therefore, the potential is increasing.

3) If the path is perpendicular to the electric field, electric potential does not change.

:Question: Location 1 is at <.1,0,0> and Location 2 is at <.5,0,0>. The uniform electric field is <0,300,0> N/C. The charge travels from Location 1 to Location 2.

:new dL = <.5,0,0> - <.1,0,0> = <.4,0,0>m
:dV = -(Exdx + Eydy + Exdz) = -(.4*0 + 0*300 +0*0) = 0 V

:Answer: 0V

:Ex 2: Figure 1
- Refer back to the figure 1 above. If the path is going from point B to C, or (point A to D), these points are perpendicular to the electric field. Because no work is required to move a
a charge between them, all points that are perpendicular to same electric field share same electric potential.

===Difficult===

The difficult example will refer to using a path that is not directly parallel to the electric field.

Question: Assume an electric field that has a magnitude of 300 N/C. The electric field is uniform. The path chosen is 5 m, 50 degrees away from the field. What is the difference in electric potential in this situation?

:dV = -E*dl = -E*l*cos(theta)
:dV = -(300 N/C)*(5 m)*cos(50) = -964 V

Answer: -964 V

==Connectedness==

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

:Potential difference is extremely applicable and interesting to me because I am a computer engineer and as a computer engineer, I deal with many things regarding electricity. I am particularly interested in building electric guitar pedals. In addition to the digital signal processing and programming aspect of guitar pedals, there is a lot of physics involved with how they work. Potential difference and electric potential kick in because in addition to the signals that are transmitted throughout the TRS cables, current also runs through them. Obviously, energy and charge are also very prominent in this so they are directly applied to the construction of guitar pedals.

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

:As a computer engineer, in class and ideally in my job after college, I will be dealing with electronics and electricity in action. I am constantly dealing with breadboards, semiconductors, microprocessors, cables, etc. All of these things essentially require a basic understanding of physics topics especially related to electromagnetism.

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

:An interested industrial application of electric potential is the ability to use electric potential sensors in human body electrophysiology. In a study conducted by the Center for Physical Electronics and Quantum Technology, the team utilized these sensors to detect electric signals in the human body. The sensors were mainly built with electrometer amplifiers. Specific to electric potential, the senors focus on displacement current rather than electric current at certain locations. The following signals were detected: electrocardiograms, electroencephalograms, and electro-oculograms, and the sensors were able to find the three signals without directly touching the human body. With these findings, the scientists are able to create "spatio-temporal array imaging" of different areas of the human body, including the heart and brain!

==History==

-Alessandro Volta, and Italian physicist, contributed many ideas and inventions to the field of electricity. He invented the first electric battery, the first electromotive series, and most notably, contributed to the idea of electric potential and its unit, the volt.

-In 1745, Volta was born. He spent most of his childhood experimenting with electricity in his friend's physics lab. When he was 18, he started communicating with physicists, Jean-Antonie Nollet and Giambatista Beccaria, who encouraged him to continue with his experiments.

-In 1775, Volta began teaching physics. He soon was able to isolate methane gas, which he discovered could produce electric sparks. In 1776, Volta put the two ideas together to conclude that he could send electric signals across Italy with the sparking machine.

-In 1778, Volta discovered electric potential, or voltage. He realized that the electric potential in a capacitor is directly proportional to the electric charge in that capacitor.

-In 1800, Volta combined all of his findings to create the voltaic pile, or the first electrochemical cell. This battery made of zinc and copper was able to produce a steady and constant electric current.

-Batteries today serve as the major practical application of electric potential. The unit for electric potential, the Volt, is named after Alessandro Volta and his contributions to the field of electricity.

== See also ==

===Further reading===

'''Books, Articles or other print media on this topic'''

-Electric Potential Difference across a cell membrane:
:https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=electric+potential+difference+journal+articles

-Electric Potential Difference between ion phases:
:http://pubs.acs.org/doi/abs/10.1021/j150300a003

===External links===

'''Internet resources on this topic'''

This video that walks through examples on potential difference in a uniform field:
:https://www.youtube.com/watch?v=mF3VAjcjvOA

This video further discusses electric potential and its concepts:
:https://www.youtube.com/watch?v=wT9AsY79f1k

This video on electric potential energy gives a good background on solving problems before learning specifically about electric potential:
:https://www.khanacademy.org/science/physics/electric-charge-electric-force-and-voltage/electric-potential-voltage/v/electric-potential-energy

==References==

-http://study.com/academy/lesson/what-is-electric-potential-definition-formula-quiz.html

-http://www.famousscientists.org/alessandro-volta/

-http://www.isipt.org/world-congress/3/269.html

-http://maxwell.ucdavis.edu/~electro/potential/overview.html

-Matter & Interactions Vol II: Electric and Magnetic Interactions textbook

[[Category:Fields]]

Potential Difference in a Uniform Field

2017-04-10T00:04:01Z

Emilypark: /* Middling */

By: dachtani3

'''CLAIMED BY SHAN SUEN (FALL 2016) (edited main idea, revised mathematical model, added more reference links, edited some connectedness)'''
Claimed by SeongEun Park April, 2017

Electric potential is a scalar quantity that is used to describe the change in electric potential energy per unit charge. This page will elaborate on the change in electric potential in a uniform field.

==The Main Idea==

Potential difference is the change in electric potential between a final and initial location when work is done on a charge to to affect its potential energy. The unit for electric potential is a volt (which is also joule/coulomb). Approximation of uniform field is useful for simple calculation.

===A Mathematical Model===

This equation represents potential difference, where V is electric potential, U is electric potential energy, and q is unit charge.
The unit for electric potential is 'V' (volt), where it takes 1 Joules of work to move 1 Coulomb of unit charge per 1 volt.
:<math>\Delta V</math> = <math>\frac{dU}{q} </math>

You can rearrange this equation to also show that electric potential energy is electric potential times unit charge.
:<math>\Delta U</math> = <math>q \Delta V</math>

In addition, you can express electric potential as the sum of the dot product of electric field and displacement in each dimension. This expression is as follows:
:<math>\Delta V</math> = -<math>\vec{E}</math>●<math>\Delta \vec{l}</math> = -(<math>E_{x}</math>●<math>\Delta x</math> + <math>E_{y}</math>●<math>\Delta y</math> + <math>E_{z}</math>●<math>\Delta z</math>)
You can also use dot product notation:
:<math>\Delta V</math> = -<math>\vec{E}</math>●<math>\Delta \vec{l}</math> = <math> (E_{x},E_{y},E_{z})●(dX, dY, dZ) </math>

Potential difference can be either positive or negative because each component of electric field and displacement can be positive or negative. Within this expression, you can also note that the units for the electric field are V/m. We originally learned that units for electric field are N/c, but V/m is also an appropriate unit.

===A Computational Model===

This video showcases 3D-models of the interaction of charges with electric potential and electric potential energy. This video is especially helpful if you want to learn these topics conceptually.

https://www.youtube.com/watch?v=-Rb9guSEeVE

In addition, this image showcases the relationship between electric fields and electric potential. If you take the negative gradient of electric potential, the result is the electric field. The gradient is the direction of the hills seen in the graph representing electric potential.

[[File:3-d_model.jpg]]

==Examples==

===Simple===

Questions 1 and 2 are based on the following situation:

A path consists of two locations. Location 1 is at <0.1,0,0>m and Location 2 is at <0.5,0,0>m. A uniform electric field of <300,0,0> N/C exists in this region pointing from Location 1 to Location 2.

Question 1: What is the difference in electric potential between the two points?

:<math>\Delta{L}</math> = final location - initial location = <0.5, 0,0 > - <0.1, 0, 0> = <0.4, 0, 0> m
:<math>\Delta{V}</math> = -<math>\vec{E}</math>●<math>\Delta \vec{l}</math> = -(<math>E_{x}</math>●<math>\Delta x</math> + <math>E_{y}</math>●<math>\Delta y</math> + <math>E_{z}</math>●<math>\Delta z</math>)
= -(300 N/C*.4 + 0*0 + 0*0)
= -120

Answer: -120 V

Question 2: What is the change in electric potential energy for a proton on this path?

:dU = dV*q = -120 V * 1.6e-19 C = -1.92e-17 J

Answer: - 1.92e-17 J

===Middling===
[[File:Slide1.jpg]]

Key Point to remember about signs:

1) If the path is going in the direction of the electric field, electric potential is decreasing.

:Ex: Refer to Simple Example
:Ex 2: Figure 1
- Consider the path going from point A to point B. The path is in the same direction as the electric field (red arrow).
Because ΔV = -E●Δl = -E●Δr(A->B) = -E●d. This then refers ΔV = Vb-Va < 0, meaning that the electric potential is decreasing.

2) If the path is going in the opposite direction of the electric field, electric potential is increasing.

:Question: Location 1 is at <.1,0,0> and Location 2 is at <.5,0,0>. The uniform electric field is <300,0,0> N/C. The charge travels from Location 2 to Location 1.

:new dl = <.1,0,0> - <.5,0,0> = <-.4,0,0>m
:dV = -Exdx = -(-.4*300) = +120V

:Answer: + 120 V

:Ex 2: Figure 1
- Refer back to the figure 1 above. If the path from point C to D was taken, it is going in the opposite direction of the electric field, which means that ΔV > 0;
therefore, the potential is increasing.

3) If the path is perpendicular to the electric field, electric potential does not change.

:Question: Location 1 is at <.1,0,0> and Location 2 is at <.5,0,0>. The uniform electric field is <0,300,0> N/C. The charge travels from Location 1 to Location 2.

:new dL = <.5,0,0> - <.1,0,0> = <.4,0,0>m
:dV = -(Exdx + Eydy + Exdz) = -(.4*0 + 0*300 +0*0) = 0 V

:Answer: 0V

:Ex 2: Figure 1
- Refer back to the figure 1 above. If the path is going from point B to C, or (point A to D), these points are perpendicular to the electric field. Because no work is required to move a
a charge between them, all points that are perpendicular to same electric field share same electric potential.

===Difficult===

The difficult example will refer to using a path that is not directly parallel to the electric field.

Question: Assume an electric field that has a magnitude of 300 N/C. The electric field is uniform. The path chosen is 5 m, 50 degrees away from the field. What is the difference in electric potential in this situation?

:dV = -E*dl = -E*l*cos(theta)
:dV = -(300 N/C)*(5 m)*cos(50) = -964 V

Answer: -964 V

==Connectedness==

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

:Potential difference is extremely applicable and interesting to me because I am a computer engineer and as a computer engineer, I deal with many things regarding electricity. I am particularly interested in building electric guitar pedals. In addition to the digital signal processing and programming aspect of guitar pedals, there is a lot of physics involved with how they work. Potential difference and electric potential kick in because in addition to the signals that are transmitted throughout the TRS cables, current also runs through them. Obviously, energy and charge are also very prominent in this so they are directly applied to the construction of guitar pedals.

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

:As a computer engineer, in class and ideally in my job after college, I will be dealing with electronics and electricity in action. I am constantly dealing with breadboards, semiconductors, microprocessors, cables, etc. All of these things essentially require a basic understanding of physics topics especially related to electromagnetism.

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

:An interested industrial application of electric potential is the ability to use electric potential sensors in human body electrophysiology. In a study conducted by the Center for Physical Electronics and Quantum Technology, the team utilized these sensors to detect electric signals in the human body. The sensors were mainly built with electrometer amplifiers. Specific to electric potential, the senors focus on displacement current rather than electric current at certain locations. The following signals were detected: electrocardiograms, electroencephalograms, and electro-oculograms, and the sensors were able to find the three signals without directly touching the human body. With these findings, the scientists are able to create "spatio-temporal array imaging" of different areas of the human body, including the heart and brain!

==History==

-Alessandro Volta, and Italian physicist, contributed many ideas and inventions to the field of electricity. He invented the first electric battery, the first electromotive series, and most notably, contributed to the idea of electric potential and its unit, the volt.

-In 1745, Volta was born. He spent most of his childhood experimenting with electricity in his friend's physics lab. When he was 18, he started communicating with physicists, Jean-Antonie Nollet and Giambatista Beccaria, who encouraged him to continue with his experiments.

-In 1775, Volta began teaching physics. He soon was able to isolate methane gas, which he discovered could produce electric sparks. In 1776, Volta put the two ideas together to conclude that he could send electric signals across Italy with the sparking machine.

-In 1778, Volta discovered electric potential, or voltage. He realized that the electric potential in a capacitor is directly proportional to the electric charge in that capacitor.

-In 1800, Volta combined all of his findings to create the voltaic pile, or the first electrochemical cell. This battery made of zinc and copper was able to produce a steady and constant electric current.

-Batteries today serve as the major practical application of electric potential. The unit for electric potential, the Volt, is named after Alessandro Volta and his contributions to the field of electricity.

== See also ==

===Further reading===

'''Books, Articles or other print media on this topic'''

-Electric Potential Difference across a cell membrane:
:https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=electric+potential+difference+journal+articles

-Electric Potential Difference between ion phases:
:http://pubs.acs.org/doi/abs/10.1021/j150300a003

===External links===

'''Internet resources on this topic'''

This video that walks through examples on potential difference in a uniform field:
:https://www.youtube.com/watch?v=mF3VAjcjvOA

This video further discusses electric potential and its concepts:
:https://www.youtube.com/watch?v=wT9AsY79f1k

This video on electric potential energy gives a good background on solving problems before learning specifically about electric potential:
:https://www.khanacademy.org/science/physics/electric-charge-electric-force-and-voltage/electric-potential-voltage/v/electric-potential-energy

==References==

-http://study.com/academy/lesson/what-is-electric-potential-definition-formula-quiz.html

-http://www.famousscientists.org/alessandro-volta/

-http://www.isipt.org/world-congress/3/269.html

-http://maxwell.ucdavis.edu/~electro/potential/overview.html

-Matter & Interactions Vol II: Electric and Magnetic Interactions textbook

[[Category:Fields]]

File:Figure1.jpg

2017-04-10T00:02:52Z

Emilypark: figure1

figure1

File:Slide1.jpg

2017-04-10T00:02:21Z

Emilypark: Emilypark uploaded a new version of "File:Slide1.jpg"

File:Slide1.jpg

2017-04-10T00:00:43Z

Emilypark: Emilypark uploaded a new version of "File:Slide1.jpg"

2017-04-09T22:35:25Z

Emilypark:

''Claimed by Josh Whitley Spring 2016, Edited by Emilie Pourchet Fall 2016''

The concept of potential difference relies on what we call "Path Independence". This means that the path taken between the two observed locations does not affect the potential difference between the two locations. Therefore, any path can be taken to calculate the potential difference between two points. This can be very useful in some calculations, as will be shown later.

==The Main Idea==

=What is Electric Potential?=
In order to understand why the electric potential difference is path independent, it can be helpful to define electric potential.

Electric potential is the amount of electric potential energy that a point charge would have if it was located at some point in space (point B in this wiki page is how I will refer to this point in space), relative to an arbitrary reference point (point A). It equals the work done by a constant external force in carrying the charge from point A to point B. Note that this does mean moving a point charge around in space before returning it to its original location means both the work done and the potential equal 0. Electric potential is measured in volts or Joules/Coulomb. Electric potential at infinity is effectively 0.

=What is Path Independence?=
Electric potential, as stated above, is entirely independent of the path taken to get from an initial to final state. When presented with a complex path from one point to another, choosing the easiest path (a straight line connecting the two points) can simplify the problem while still yielding the correct answer as a result of this principle.

Note that path independence holds true for all potential energy, not just electric potential. For that reason, a useful frame of reference is the path independence of physical objects' potential energy in a gravitic field that is introduced in physics 1 - electric potential path independence functions the same way.

===A Mathematical Model===

The general representation of electric potential is the following:

<math> \triangle V = V_b-V_a </math>

This formula can be expanded by summing the different components of the change in position within electric field components to calculate the change in electric potential. This equation is useful for proving path independence as it can be applied to multi-step path in straight line increments, proving when compared to a direct path that the change in electric potential is the same.

<math> \triangle V = -(E_x \triangle x, E_y \triangle y, E_z \triangle z) </math>

===A Computational Model===

[https://trinket.io/glowscript/8d8cbfc025]

Click the above link to go to a GlowScript page that details Path Independence of Electric Potential. Point A is marked by a green sphere, Point B is marked by a red sphere, moving negative particle 1 is marked by a blue sphere and trail, while moving negative particle 2 is marked by a white sphere and trail. Remember to scroll down in the display window to make sure you've seen the most recent printed value!

In this simulation, you can:

1) Click the display window to progress the simulation, which will print a change in electric potential below corresponding to the parameters of your electric field and the size of your movement. By default, the electric field is (-50,0,0) N/C and the steps are arbitrary and simply designed to show a progression from point A to B by the particle.

2) See how two different paths (one blue and one white) result in the same change in electric potential, regardless of their stark differences in path length.

''Note that if you have difficulty seeing the simulation or the printed values, you can navigate to the menu in the top left of the coding window (represented by three parallel bars) and engage a fullscreen mode.''
''Note also that the default code is set to use an electric field with only an x component, for simplicity. Changes in the size of the movement steps are not supported.''

==Examples==
=Example 1=
Below is an example that demonstrates the path independence of electric potential difference.

[[File:phys1.jpg]] [[File:Phys2.jpg]]

Let's calculate the potential difference between A and B in the first scenario. Assume that the height difference between A and B is y and the x component increases by x.

<math> \triangle V= -(E_x \triangle x, E_y \triangle y, E_z \triangle z) </math>

<math> \triangle V= -E_x(x_1-0) + 0(y_1-0) + 0*0 </math>

<math> \triangle V = -E_xx_1 </math>

In the second scenario, let's divide this process into two parts to follow the path outlined from A to C and from C to B.

'''From A to C:'''

<math> \triangle V = -(E_x \triangle x, E_y \triangle y, E_z \triangle z) </math>

<math> \triangle V = -E_x(x_1-0)+ 0*0 + 0*0 </math>

<math> \triangle V = -E_xx_1</math>

'''From C to B:'''

<math> \triangle V = -(E_x \triangle x, E_y \triangle y, E_z \triangle z) </math>

<math> \triangle V = -E_x*0 + 0*(y-0) + 0*0 </math>

<math> \triangle V = 0 </math>

Now let's calculate the TOTAL potential difference for this scenario, it is the sum of the potential differences from A to B and from B to C.

<math> \triangle V_{A to B} = \triangle V_{A to C} + \triangle V_{C to B} </math>

<math> \triangle V_{total} = -E_xx_1 + 0 = -E_xx_1 </math>

We can see that the results for both scenarios are the same, therefore the electric potential difference is independent of the path taken to calculate it.

=Example 2=

[[File:Prob1.jpg]]

The above problem deals with a triple-plated, double-spaced, and parallel-plated capacitor and the associated potential difference as you cross over the center plate. Note that, intuitively, the electric fields are only multiplied by the portion of the path that falls within their respective capacitor space. They are then summed. This problem also deals with potential difference when path is reversed.

In order to make this problem demonstrate Path Independence specifically, simply take a new path from A to B (by creating points in between) and calculate the displacement components times the corresponding electric field component of those mid points instead of the direct A to B path. You will find that all Y and Z components equal 0, which leaves only the X component of the path to be calculated. This will inevitably end up with the same potential difference as what is done above.

==Connectedness==
''How is this topic connected to something that you are interested in? How is it connected to your major?''

Spontaneous redox reactions often cause a potential disparity that can drive batteries. Electrochemistry, a subset of chemistry that I am interested in as an aspiring chemical engineer, spends a significant amount of time focusing on these interactions and the electrical output of different reaction combinations. In a sense, understanding the physics side of electrical potential helps round out my understanding of electrochemistry.

''Is there an interesting industrial application?''

In terms of strictly applying the idea of path independence, I would argue there is no industrial application. Though I would argue that related fields, such as electrochemistry, have sweeping industrial applications. The optimization of batteries relies partially on finding half reaction combinations that yield the largest positive potential. It's just that strictly dealing with path independence doesn't leave much room for innovation or invention - you need to involve related ideas. Perhaps the pathing of chemicals inside of a battery is made moot by this principle.

==History==

Around 1800 an Italian doctor named Luigi Galvani found that touching a frog's leg to two different metals caused it to twitch. Alessandro Volta, a contemporary and rival or Galvani, studied these findings and concluded that a kind of electrical potential difference between the two metals caused a charge to flow through the frog's leg, firing the muscles to ultimately create a post-mortem twitch.

Volta found that, in the presence of significant electrical potential between two metals, electrical charge can flow through a metal wire (and through frog legs, salinated brine, etc). The analogy of the time was that current flowed through wire similarly to water in a pipe. Because of this discovery, Volta lives on through the concept of voltage and the associated unit of measurement - the volt.

== See also ==

https://en.wikipedia.org/wiki/Voltage#See_also

https://en.wikipedia.org/wiki/Electric_potential

https://www.insidescience.org/content/soccers-electric-potential/1022

http://jes.ecsdl.org/content/147/11/4263.abstract

http://farside.ph.utexas.edu/teaching/302l/lectures/node32.html

http://faculty.cua.edu/sober/611/PATHIND.pdf

http://scienceline.ucsb.edu/getkey.php?key=4026

==References==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

Chapter 16 Webassign Review

http://scienceline.ucsb.edu/getkey.php?key=4026

[[Category:Energy]]

Path Independence of Electric Potential

2017-04-09T22:29:51Z

Emilypark:

''Claimed by Josh Whitley Spring 2016, Edited by Emilie Pourchet Fall 2016''
Claimed by SeongEun Park April, 2017

The concept of potential difference relies on what we call "Path Independence". This means that the path taken between the two observed locations does not affect the potential difference between the two locations. Therefore, any path can be taken to calculate the potential difference between two points. This can be very useful in some calculations, as will be shown later.

==The Main Idea==

=What is Electric Potential?=
In order to understand why the electric potential difference is path independent, it can be helpful to define electric potential.

Electric potential is the amount of electric potential energy that a point charge would have if it was located at some point in space (point B in this wiki page is how I will refer to this point in space), relative to an arbitrary reference point (point A). It equals the work done by a constant external force in carrying the charge from point A to point B. Note that this does mean moving a point charge around in space before returning it to its original location means both the work done and the potential equal 0. Electric potential is measured in volts or Joules/Coulomb. Electric potential at infinity is effectively 0.

=What is Path Independence?=
Electric potential, as stated above, is entirely independent of the path taken to get from an initial to final state. When presented with a complex path from one point to another, choosing the easiest path (a straight line connecting the two points) can simplify the problem while still yielding the correct answer as a result of this principle.

Note that path independence holds true for all potential energy, not just electric potential. For that reason, a useful frame of reference is the path independence of physical objects' potential energy in a gravitic field that is introduced in physics 1 - electric potential path independence functions the same way.

===A Mathematical Model===

The general representation of electric potential is the following:

<math> \triangle V = V_b-V_a </math>

This formula can be expanded by summing the different components of the change in position within electric field components to calculate the change in electric potential. This equation is useful for proving path independence as it can be applied to multi-step path in straight line increments, proving when compared to a direct path that the change in electric potential is the same.

<math> \triangle V = -(E_x \triangle x, E_y \triangle y, E_z \triangle z) </math>

===A Computational Model===

[https://trinket.io/glowscript/8d8cbfc025]

Click the above link to go to a GlowScript page that details Path Independence of Electric Potential. Point A is marked by a green sphere, Point B is marked by a red sphere, moving negative particle 1 is marked by a blue sphere and trail, while moving negative particle 2 is marked by a white sphere and trail. Remember to scroll down in the display window to make sure you've seen the most recent printed value!

In this simulation, you can:

1) Click the display window to progress the simulation, which will print a change in electric potential below corresponding to the parameters of your electric field and the size of your movement. By default, the electric field is (-50,0,0) N/C and the steps are arbitrary and simply designed to show a progression from point A to B by the particle.

2) See how two different paths (one blue and one white) result in the same change in electric potential, regardless of their stark differences in path length.

''Note that if you have difficulty seeing the simulation or the printed values, you can navigate to the menu in the top left of the coding window (represented by three parallel bars) and engage a fullscreen mode.''
''Note also that the default code is set to use an electric field with only an x component, for simplicity. Changes in the size of the movement steps are not supported.''

==Examples==
=Example 1=
Below is an example that demonstrates the path independence of electric potential difference.

[[File:phys1.jpg]] [[File:Phys2.jpg]]

Let's calculate the potential difference between A and B in the first scenario. Assume that the height difference between A and B is y and the x component increases by x.

<math> \triangle V= -(E_x \triangle x, E_y \triangle y, E_z \triangle z) </math>

<math> \triangle V= -E_x(x_1-0) + 0(y_1-0) + 0*0 </math>

<math> \triangle V = -E_xx_1 </math>

In the second scenario, let's divide this process into two parts to follow the path outlined from A to C and from C to B.

'''From A to C:'''

<math> \triangle V = -(E_x \triangle x, E_y \triangle y, E_z \triangle z) </math>

<math> \triangle V = -E_x(x_1-0)+ 0*0 + 0*0 </math>

<math> \triangle V = -E_xx_1</math>

'''From C to B:'''

<math> \triangle V = -(E_x \triangle x, E_y \triangle y, E_z \triangle z) </math>

<math> \triangle V = -E_x*0 + 0*(y-0) + 0*0 </math>

<math> \triangle V = 0 </math>

Now let's calculate the TOTAL potential difference for this scenario, it is the sum of the potential differences from A to B and from B to C.

<math> \triangle V_{A to B} = \triangle V_{A to C} + \triangle V_{C to B} </math>

<math> \triangle V_{total} = -E_xx_1 + 0 = -E_xx_1 </math>

We can see that the results for both scenarios are the same, therefore the electric potential difference is independent of the path taken to calculate it.

=Example 2=

[[File:Prob1.jpg]]

The above problem deals with a triple-plated, double-spaced, and parallel-plated capacitor and the associated potential difference as you cross over the center plate. Note that, intuitively, the electric fields are only multiplied by the portion of the path that falls within their respective capacitor space. They are then summed. This problem also deals with potential difference when path is reversed.

In order to make this problem demonstrate Path Independence specifically, simply take a new path from A to B (by creating points in between) and calculate the displacement components times the corresponding electric field component of those mid points instead of the direct A to B path. You will find that all Y and Z components equal 0, which leaves only the X component of the path to be calculated. This will inevitably end up with the same potential difference as what is done above.

==Connectedness==
''How is this topic connected to something that you are interested in? How is it connected to your major?''

Spontaneous redox reactions often cause a potential disparity that can drive batteries. Electrochemistry, a subset of chemistry that I am interested in as an aspiring chemical engineer, spends a significant amount of time focusing on these interactions and the electrical output of different reaction combinations. In a sense, understanding the physics side of electrical potential helps round out my understanding of electrochemistry.

''Is there an interesting industrial application?''

In terms of strictly applying the idea of path independence, I would argue there is no industrial application. Though I would argue that related fields, such as electrochemistry, have sweeping industrial applications. The optimization of batteries relies partially on finding half reaction combinations that yield the largest positive potential. It's just that strictly dealing with path independence doesn't leave much room for innovation or invention - you need to involve related ideas. Perhaps the pathing of chemicals inside of a battery is made moot by this principle.

==History==

Around 1800 an Italian doctor named Luigi Galvani found that touching a frog's leg to two different metals caused it to twitch. Alessandro Volta, a contemporary and rival or Galvani, studied these findings and concluded that a kind of electrical potential difference between the two metals caused a charge to flow through the frog's leg, firing the muscles to ultimately create a post-mortem twitch.

Volta found that, in the presence of significant electrical potential between two metals, electrical charge can flow through a metal wire (and through frog legs, salinated brine, etc). The analogy of the time was that current flowed through wire similarly to water in a pipe. Because of this discovery, Volta lives on through the concept of voltage and the associated unit of measurement - the volt.

== See also ==

https://en.wikipedia.org/wiki/Voltage#See_also

https://en.wikipedia.org/wiki/Electric_potential

https://www.insidescience.org/content/soccers-electric-potential/1022

http://jes.ecsdl.org/content/147/11/4263.abstract

http://farside.ph.utexas.edu/teaching/302l/lectures/node32.html

http://faculty.cua.edu/sober/611/PATHIND.pdf

http://scienceline.ucsb.edu/getkey.php?key=4026

==References==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

Chapter 16 Webassign Review

http://scienceline.ucsb.edu/getkey.php?key=4026

[[Category:Energy]]