Check out the equipotential surfaces of a bunch of charges dancing around each other.

https://www.youtube.com/watch?v=8JpwAKE69BM

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 Potential  |  Charges in a Field and the Total Energy of a System of Charges

Positive charges feel a force and speed up in the direction of decreased electric potential.

It's because that decreases the electric potential energy. All particles feel a force in the direction of decreased potential energy, but be careful, for a negative charge, it feels a force toward increased electric potential because that actually decreases the electric potential energy. The minus sign on the charge accounts for the difference between the positive charge moving towards decreased potential while the negative charge moves towards increased potential. Both do so to decrease the potential energy.

This example also illustrates the power of the field concept. Once we have found the electric potential field from a charge distribution, we can perform an infinite number of theoretical experiments on how much energy is converted between kinetic and potential for of any charge moving between locations in space. To make it more tangible, lets connect to the analogy of the gravitational field and gravitational potential energy. Recall that gravitational potential energy $U^g = mgh$. The gravitational field is equal to $gh$ and when multiplied by the mass you get the gravitational potential energy $mgh$. Since $g$ is a constant, the field really only depends on your height (or elevation). A topographical map is essentially a gravitational potential map.

This is an image of comparing a voltage map to a topographic map. On the voltage map there are diagonal equipotential lines which are similar to a topographic map where the lines show equal levels or elevations.

Lines (or really surfaces) called equipotentials can be used to describe places that have a constant potential and thus energy. Masses feel a force that make them want to move down the equipotentials, analogous to the positive charge above feeling a force towards decreased electric potential. In both cases (charges and masses) the systems move towards decreased potential energy. This is one of the most fundamental statements that can be made in physics - systems drive towards decreased potential energy. This is why water runs downhill.

Total Potential Energy of a Collection of Particles

One question that often arises is what is the total electric potential energy of a collection of particles. Imagine a single positive charge fixed in space. To bring a second charge close to the first, you'd have to do work to overcome the repelling force. If you did overcome that work and brought them next to each other, if they were released, they would fly away with kinetic energy. That kinetic energy comes originally from the work of bringing them together, which is converted into potential energy when they are close together. That potential energy can be thought of as the energy of the system. If you where to bring in more charges, you'd have to figure out the potential energy of all the combinations particles. The total potential energy for a system of three particles is described below.

This is an image titled total potential energy of a system: energy to bring all q’s together. It shows three charged ions in a triangular formation. The first is positively charged labeled q one on the bottom left and the second is negatively charged labeled q two on the top right and directly below is a positively charged ion called q three. It shows three different equations of the different potential forces acting on each particle. The first equation is the potential energy of one and two which is equal to the voltage of one at r two multiplied by q two which is also equal to k multiplied by q one and q two all divided by the distance between ion one and two. The appropriate equations are also written for two and three as well as one and three.

The total potential energy of the system of three particles is just summation of all the combinations. *Warning* don't over count interactions, $U_{12}$ is the total energy of the 1 and 2 system, meaning if you were to also include $U_{21}$, you'd be double counting. So it's only the unique pairs and the ordering of the subscripts does not matter.

$U_{total}=U_{12} + U_{23} +U_{13}$    ... + all combinations if there are more particles

This is how much energy would be released into kinetic energy if the system was released from rest. Notice that if there were negative charges present you could have a negative total potential energy. Systems with a negative potential energy are said to be bound systems as the particles have a net attraction to one another. They want to clump together as opposed to fly apart.


Key Equations and Infographics

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

OpenStax Reading


OpenStax Section 19.4  |  Equipotential Lines

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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
The Physics Classroom Icon The Physics Classroom Icon

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.

 

 

 

CLICK HERE for solutions.

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

BoxSand practice problems - Answers

BoxSand's conceptual problems

BoxSand's multiple select problems

BoxSand's quantitative problems

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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