Electric Potential

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations

Student Learning Objectives

To introduce electric potential energy and use it in conservation of energy problems.
To define the electric potential.
To find and use the electric potential of point charges, charged spheres, and parallel-plate capacitors.
To find the electric potential of a continuous distribution of charge.
To introduce and use potential graphs and equipotential surfaces.
To study the properties of conductors in electrostatic equilibrium.
To establish the relationship between and V.
To introduce batteries as a practical source of potential difference.
To understand the importance of symmetry.
To calculate electric flux.
To use Gauss’s law to derive several electric fields of interest.
To analyze simple capacitor circuits.
To understand capacitors and dielectrics.

Lessons / Lecture Notes

The Physics Classroom (conceptual)

Electric Potential Difference

PY106 Notes from Boston University (algebra-based):

Physics 2B notes from Dr. Bobby W.S. Lau (algebra-based)

HyperPhysics (calculus-based)

Voltage

Physics 4B notes from Dr. Bobby W.S. Lau (calculus-based)

Important Equations (for algebra-based Physics)



word	pdf

Example Problems

Example Problems for algebra-based physics (from College Physics 2nd Edition by Knight, Jones, and Field):

Example Problems (Electric Potential)
Solutions to Example Problems (Electric Potential)

Example Problems for calculus-based physics (from Fundamentals of Physics 9th Edition by Halliday, Resnick, and Walker):

Example Problems (Electric Potential) | Example Problems (Capacitance)
Solutions to Example Problems (Electric Potential) | Solutions to Example Problems (Capacitance)

Applets and Animations

John Travoltage Play with John’s foot and arm to explore when he gets a zap!

Van De Graff Generator Very cool applet showing a Van De Graff genertaor and various set-ups that you can implement.

Electric Fields in Two DImensions
This java applet displays the electric field in various situations. You may select one of many fields from the Setup menu in the upper right.

The applet shows the potential surface of the field, with particles following the field vectors. You may click and drag with the mouse to rotate the view. Also some of the field selections have parameters which may be adjusted.

Electric Fields in Three DImensions
This java applet is an electrostatics demonstration which displays the electric field in a number of situations. You can select from a number of fields and see how particles move in the field if it is treated as either a velocity field (where the particles move along the field lines) or an actual force field (where the particles move as if they were charged particles). This helps you visualize the field.

The menu in the upper right has a variety of different fields to choose from.

Electric Field and Electric Potential Click-and-drag the particles to move them left or right. The particle on the left is confined to the region to the left of the origin; the particle on the right is confined to the region to the right of the origin. In this simulation, you can see the graph of the electric field on the x-axis as a function of position, as well as the electric potential on the x-axis as a function of position. On the graph, the electric field is shown as positive if the net field at that position is directed to the right, and the field is shown as negative if the field is directed left. Using the sliders, you can adjust the charges of the particles.

Puzzle - Determine the Charges
In this simulation, the two charged particles (in green) are each randomly assigned a sign and a magnitude that is either 1, 2, 3, 4, or 5 nC. Your goal is to determine their charges, with the help of the graphs - when you have figured out what they are, set the charge sliders to those values and check your answer.

You can click-and-drag the particles to move them left or right. The particle on the left is confined to the region to the left of the origin; the particle on the right is confined to the region to the right of the origin. In this simulation, you can see the graph of the electric field on the x-axis as a function of position, as well as the electric potential on the x-axis as a function of position. On the graph, the electric field is shown as positive if the net field at that position is directed to the right, and the field is shown as negative if the field is directed left. Using the sliders, you can adjust the charges of the particles.

Potential Energy Click-and-drag the particles to move them left or right. The particle on the left is confined to the region to the left of the origin; the particle on the right is confined to the region to the right of the origin. In this simulation, you can see the graph of the electric field on the x-axis as a function of position, as well as the electric potential on the x-axis as a function of position. On the graph, the electric field is shown as positive if the net field at that position is directed to the right, and the field is shown as negative if the field is directed left. Using the sliders, you can adjust the charges of the particles.

Connections between Force, Field, Potential Energy, and Potential On the left is a representation of a 4 m x 4 m space in which there is a uniform field directed down. If you choose a ball, then the field is a gravitational field. If you use a charge, the field is an electric field. On the right is a graph. You can plot six different things on the vertical axis, as a function of either x or y.

E,V Graphs Some useful graphs showing variation of potential and field strengths with distance.
In the case of the shell charge on the shell is assumed constant and in case of the sphere charge density is assumed constant.
In case of concentric shells the charge on the outer shell is double the charge on the inner shell.
Radius of the shell/sphere/inner shell can be decreased/increased by taps on left/right halves of the graph.

John Travoltage		Play with John’s foot and arm to explore when he gets a zap!
Van De Graff Generator		Very cool applet showing a Van De Graff genertaor and various set-ups that you can implement.
Electric Fields in Two DImensions		This java applet displays the electric field in various situations. You may select one of many fields from the Setup menu in the upper right. The applet shows the potential surface of the field, with particles following the field vectors. You may click and drag with the mouse to rotate the view. Also some of the field selections have parameters which may be adjusted.
Electric Fields in Three DImensions		This java applet is an electrostatics demonstration which displays the electric field in a number of situations. You can select from a number of fields and see how particles move in the field if it is treated as either a velocity field (where the particles move along the field lines) or an actual force field (where the particles move as if they were charged particles). This helps you visualize the field. The menu in the upper right has a variety of different fields to choose from.
Electric Field and Electric Potential		Click-and-drag the particles to move them left or right. The particle on the left is confined to the region to the left of the origin; the particle on the right is confined to the region to the right of the origin. In this simulation, you can see the graph of the electric field on the x-axis as a function of position, as well as the electric potential on the x-axis as a function of position. On the graph, the electric field is shown as positive if the net field at that position is directed to the right, and the field is shown as negative if the field is directed left. Using the sliders, you can adjust the charges of the particles.
Puzzle - Determine the Charges		In this simulation, the two charged particles (in green) are each randomly assigned a sign and a magnitude that is either 1, 2, 3, 4, or 5 nC. Your goal is to determine their charges, with the help of the graphs - when you have figured out what they are, set the charge sliders to those values and check your answer. You can click-and-drag the particles to move them left or right. The particle on the left is confined to the region to the left of the origin; the particle on the right is confined to the region to the right of the origin. In this simulation, you can see the graph of the electric field on the x-axis as a function of position, as well as the electric potential on the x-axis as a function of position. On the graph, the electric field is shown as positive if the net field at that position is directed to the right, and the field is shown as negative if the field is directed left. Using the sliders, you can adjust the charges of the particles.
Potential Energy		Click-and-drag the particles to move them left or right. The particle on the left is confined to the region to the left of the origin; the particle on the right is confined to the region to the right of the origin. In this simulation, you can see the graph of the electric field on the x-axis as a function of position, as well as the electric potential on the x-axis as a function of position. On the graph, the electric field is shown as positive if the net field at that position is directed to the right, and the field is shown as negative if the field is directed left. Using the sliders, you can adjust the charges of the particles.
Connections between Force, Field, Potential Energy, and Potential		On the left is a representation of a 4 m x 4 m space in which there is a uniform field directed down. If you choose a ball, then the field is a gravitational field. If you use a charge, the field is an electric field. On the right is a graph. You can plot six different things on the vertical axis, as a function of either x or y.
E,V Graphs		Some useful graphs showing variation of potential and field strengths with distance. In the case of the shell charge on the shell is assumed constant and in case of the sphere charge density is assumed constant. In case of concentric shells the charge on the outer shell is double the charge on the inner shell. Radius of the shell/sphere/inner shell can be decreased/increased by taps on left/right halves of the graph.