1. Review of Work
Work Done on a Point Charge by a Point Charge
Potential Energy and Potential of Point Charges
Potential Energy and Potential of Many Point Charges
Relationship between Force, Field, Energy, Potential
Potential Surfaces
SI Units
Field and Potential Graphs
Electric Power

2. Definition of Work
Work is defined as the amount of force acting over a distance.
The unit of work is either Joules (J) or electron-volts (eV) Δr F φ

3. Example of Work y Δw Δh1 x m Δh2
The following is an example of the work done by gravity on a mass. y Δw
Δh1 x m
Δh2

4. Example of Work F (N) 1 -1 A1 X (m) 1 2 A2
This is an example using the the fact that integrals are areas under a curve.
F (N) 1 -1 A1
X (m) 1 2 A2

5. Definition of a Conservative Force
A force is conservative if the work it does on an object is zero when the object moves along a path and returns to its initial position.
Examples of conservative forces are gravity, elastic force, electricity and magnetism.
The following are not conservative: friction, tension, normal force.

6. Example of a Conservative Force
Gravity as a mass is raised and lowered 2 y
Δh2
Δh1 1 3 x m 5 4
WTOTAL = 0

7. Example of a Non-conservative Force
Friction on a block that is moving around a table y x 2 1 3 4 5
ΔL2
ΔL1 Δw m
WTOTAL = - fs (2ΔL1 + 2ΔL2 + 2Δw )

8. Consider the work necessary to put together two point charges.
The force is given by Coulomb’s Law.
The work needed to bring one charge from infinity to within a distance r12 of the other is
Don’t worry about the integral in the last equation. It is only there so that those who know calculus can see where the other part came from.

9. The potential energy held between these two point charges is then
Now we consider the same relationship, but with electric field instead of force. This we call the potential.
Since , then we see that

10. What if there are more point charges?1 1 2 2 3 3

11. Example 1 1 2 2 3 3

12. What about potential? 1 1 2 2 3 3

13. Example 1 1 2 2 3 3

14. Equation for Point Charges
Relationship between Work, Potential Energy, Force and Potential
The table below represents the fundamental equations of electricity all of which a derived from the electric field E.
Quantity
General Equation
Equation for Point Charges
Electric Field
Force
Potential

15. A surface is an equipotential surface if the electric potential at every point on the surface is the same.
As charges move on an equipotential surface the electric force does no work.
The electric field at a point is always perpendicular to the equipotential surface on which the point lies.
The electric field always points in the direction of decreasing potential.
Java Applet
This Applet can be found at

16. Electric Potential V J/C Electric Field V/m N/C Energy or Work eV J
Common SI Units in Electricity
Electric
Potential V
J/C
Electric Field
V/m
N/C
Energy or Work eV J

17. Relationship Electric Potential and Electric Field
The electric field is the slope of the electric potential. V
slope of this line is -E s

18. Relationship Electric Potential and Electric Field
The electric potential is the area under the curve of electric field.
positive area E s
negativearea

19. What is electric power?
Power is the change in work over time
We will use this latter when we reach the topic in circuits.

20. What is electric power?
Power is the change in work over time
We will use this latter when we reach the topic in circuits.