It is easy to measure the electric potential using a volt meter. If you can map out the voltage in some region of space, you can determine the electric field from that voltage map. It is in this way that once you know the electric potential, you know everything.

https://www.youtube.com/watch?v=Trygmjbk_c4

Pre-lecture Study Resources

Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class.

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Learning Objectives

Summary

Summary

Atomistic Goals

Students will be able to...

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BoxSand Introduction

Electric Potentials  |  Connecting the Electric Potential and Field

Connecting the Electric Potential and the Electric Field

The electric field and potential have a close relationship. In 1-D the electric field can be thought as negative the slope of the electric potential.

$\bar{E}_x = -\frac{\Delta V}{\Delta x}$

Lessons from the above equation are:

   1) if $\frac{\Delta V}{\Delta x} = constant$ (linear), then $E_x$ is constant and uniform, this is the case near large sheets of charge and in parallel plate capacitors.

   2) The relationship between the electric field and potential is independent of the test charge $q_0$ - it's independent of other charges interacting with the field

   3) The minus sign tells us the electric field points towards decreasing electric potential - if $\frac{\Delta V}{\Delta x}$ is negative, $E_x$ is positive

In 3-D the electric field is negative the gradient of the electric potential.

$\overrightarrow{E} = - \langle \frac{\Delta V}{\Delta x}, \frac{\Delta V}{\Delta y}, \frac{\Delta V}{\Delta z} \rangle$

A gradient is a vector and can be thought of as a kind of 3-D slope that points in the direction of steepest ascent. With the minus sign the electric field points in the direction of steepest descent. Since this is the direction of the force on a positive charge we can again make the analogous connection to the gravitational field and how water is forced to run downhill, down the direction of steepest descent. This feature adds one more lesson:

   4) The electric field is perpendicular to equipotential surfaces and lines

Summary

We can now go full circle with the connections between the electric field and potential, and the electric force and energy. The electric field and potential are owned by the charge distribution and preclude any interactions with new test charges $q_0$. The electric force and potential energy require an interaction with the test charge. The concept map below helps visualize the relationship.

This is an image showing how electric field, electric potential, electric force and electric potential energy are related. The electric potential in voltage is a scalar field that is related to the electric field which is a vector field by the equation electric field is equal to the negative change in voltage divided by the change in position. The electric field which is a vector field is related to the electric force which is a vector interaction by the equation electric force is equal to q naught multiplied by the electric field. The electric force which is a vector interaction is related to the electric potential energy which is a scalar interaction by the equations the negative change in electric potential energy is equal to the electric work. Another equation to show this is the electric force dot product of the change in position (but this is only true if there is a constant electric force) and this is equal to negative electric potential energy. The electric potential energy which is a scalar interaction is related to the electric potential which is a scalar field by the equations the potential electric energy is equal to q multiplied by the voltage and the change in electric potential energy is equal to q multiplied by the change in voltage.

Key Equations and Infographics

Now, take a look at the pre-lecture reading and videos below.

OpenStax Reading


OpenStax Section 19.2  |  Electric Potential in a Uniform Electric Field

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Additional Study Resources

Use the supplemental resources below to support your post-lecture study.

YouTube Videos

 

Pre-Med Academy has a lot of videos about the Electric Field and Force, too many to list here. We really recommend checking out the content repository for this section and check out the rest of their videos Here are just a few on Work and Potential Energy, Electric Potential Difference, and Potential of a Point Charge

Youtube: Pre-Med Academy - Work and Potential Energy

Youtube: Pre-Med Academy - Electric Potential Difference

Youtube: Pre-Med Academy - Potential of a point charge

Step By Step Science has a bunch of practice problems having to do with electric potential and we suggest you check out your content repository for this section to see a list of relevant videos from them. Here are a few on work done moving a point charge through a potential difference, calculating potential difference between two points, and work to bring in a charge from infinity.

 

Youtube: Step by Step Science - charge through potential

 

Youtube: Step by Step Science - potential difference

 

Youtube: Step by Step Science - charge from infinity

 

Other Resources

This link will take you to the repository of other content related resources .

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Simulations


 

This flashphysics applet lets you create charge distributions from point charges and plot the corresponding equipotential lines.  Try placing test charges in the region of space to watch possible trajectories!

LINK THAT NEEDS IMAGE

This PhET interactive combines electric fields, electric potential and charge (known collectively as electrostatics). Place charges around and observe the resulting electric and potential fields. 

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For additional simulations on this subject, visit the simulations repository.

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Demos


For additional demos involving this subject, visit the demo repository

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History


Oh no, we haven't been able to write up a history overview for this topic. If you'd like to contribute, contact the director of BoxSand, KC Walsh (walshke@oregonstate.edu).

Physics Fun

Daybreak cover on Giant Tesla Coils

https://www.youtube.com/watch?v=mbybQX3OnZs

Other Resources


Resource Repository

The Physics Classroom has two sections for us, one on electric potential and the other on electric potential difference.

Electric Potential Electric Potential Difference
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Boston University's Page on electric potential is a neat reference with a couple of example problems

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PPLATO is a complete resource with a lot of information, and several practice questions per subject. This webpage covers electric charge, the electric field, and electric potential, we've already covered charge, and the electric field, so now it's time to focus on electric potential!

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Here's a link to Hyperphysics' reference for electric potential energy

 

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Isaac Physics' section on the electric field is a good short resource. This page contains previously studied material on electric fields as well as information on electric potential, and the connection between electric field and electric potential.

 

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Other Resources

This link will take you to the repository of other content related resources .

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This link will take you to the repository of other content related resources.

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Problem Solving Guide

Use the Tips and Tricks below to support your post-lecture study.

Assumptions

 

Checklist

 

Misconceptions & Mistakes

  • The electric potential from a point charge is proportional to $\frac{1}{r}$, not $\frac{1}{r^2}$.

Pro Tips

 

Multiple Representations

Multiple Representations is the concept that a physical phenomena can be expressed in different ways.

Physical

Physical Representations describes the physical phenomena of the situation in a visual way.

 

Mathematical

Mathematical Representation uses equation(s) to describe and analyze the situation.

A representation with the words electric potential energy on the top. There is an equation that shows that the change in potential energy of the system is equal to the test charge q naught multiplied by the change in electric potential. This is also written in words below.

 

A representation with the words electric potential from a point charge on the top. There is an equation that shows that the electric potential of a point charge q is equal to the Coulomb’s constant multiplied by the point charge divided by the distance from the point charge to the location of interest. This is also written in words below.

 

A representation with the words electric potential for a charge distribution on the top. There is an equation that shows that the total electric potential field from a group of charges is equal to the contribution from each individual particle at the location of interest. This is also written in words below.

 

A representation with the words total potential energy on the top. There is an equation that shows that the total potential energy of a system is equal to the summation of all unique combinations of individual charges. This is also written in words below with a note that says do not double count potential energy contributions.

Graphical

Graphical Representation describes the situation through use of plots and graphs.

 

Descriptive

Descriptive Representation describes the physical phenomena with words and annotations.

 

Experimental

Experimental Representation examines a physical phenomena through observations and data measurement.

 

Practice

Use the practice problem sets below to strengthen your knowledge of this topic.

Fundamental examples

 

1.  Two plates of metal with uniform charge distribution are held a distance d apart from each other as shown in the figure below.  The metal plate on the left side is positively charged while the metal plate on the right is negatively charged.

This is an image of two charged plates with the positively charged plate on the left side with a positively charged atom in front of it labeled as ion one and at some distance d to the right is a negatively charged plate with another positively charged atom in front of it labeled as ion two.



a.  Which plate is considered to be at a higher potential ($V$)?



b.  The electron labeled $1$ is placed in-between the two sheets as shown.  Does this electron have a high or low electric potential energy?  Ignore the other charges in-between the plates.  



c.  The electron labeled $2$ is placed in-between the two sheets as shown.  Does this electron have a high or low electric potential energy?  Ignore the other charges in-between the plates.



d.  The proton labeled $1$ is placed in-between the two sheets as shown.  Does this proton have a high or low electric potential energy?  Ignore the other charges in-between the plates.



e.  The proton labeled $2$ is placed in-between the two sheets as shown.  Does this proton have a high or low electric potential energy?  Ignore the other charges in-between the plates.

 

2.  Two parallel plates are held $20.0 \, mm$ apart and the potential difference between the plates is $110 \, V$. 



a.  What is the magnitude of the electric field between the two parallel plates?



b.  Which direction does the electric field point if the plate on the left has a uniform negative charge distribution and the plate on the right has a uniform positive charge distribution?



c.  Sketch a physical representation of this problem.  Include a few equipotential lines between the two parallel plates.

 

3.  Two uniformly charged parallel plates are held some distance “$d$” apart from each other with an electric potential of $300 \, V$ between them.  An electron is placed at rest near the negative charged plate.  Calculate the speed at which the electron will hit the positive plate. 

 

4.  The figure below shows a charge distribution made up of $3$ point charges.  The charges are fixed in space and cannot move.  Let $q = 1 \, \mu C$ and $L = 1.0 \, cm$.

This is an image of three different charge particles and point p all in a square formation. The bottom right corner is labeled as point p, the top right corner is a negatively charged ion called q two and has a negative charge two q. The top left corner is a positively charged ion called q one and has a positive charge q. The bottom left corner is a positively charged ion called q three and has a positive charge three q. All corners are equidistant of some distance L.



a.  Find the electric potential energy of this charge distribution.



b.  Find the electric potential at point P.

 

 

 

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Short foundation building questions, often used as clicker questions, can be found in the clicker questions repository for this subject.

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Practice Problems

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Recommended example practice problems 


For additional practice problems and worked examples, visit the link below. If you've found example problems that you've used please help us out and submit them to the student contributed content section.

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