1. Physics 212
Lecture 6
Electric Potential

2. V in Volts = Joules/Coulomb
BIG IDEA
Last time we defined the electric potential energy of charge q in an electric field:
The only mention of the particle was through its charge q.
We can obtain a new quantity, the electric potential, which is a PROPERTY OF THE SPACE, as the potential energy per unit charge.
V in Volts = Joules/Coulomb
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
Note the similarity to the definition of another quantity which is also a PROPERTY OF THE SPACE, the electric field. 40

3. Electric Potential from E field
Consider the three points A, B, and C located in a region of constant electric field as shown. D Dx
What is the sign of DVAC = VC - VA ?
(A) DVAC < (B) DVAC = (C) DVAC > 0
Remember the definition:
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
Choose a path (any will do!) 40

4. Checkpoint 2 A B C D
Remember the definition
V is constant !! 08

5. E from V We obtain the potential by integrating the electric field:
So, we can obtain the electric field by differentiating the potential.
In Cartesian coordinates:
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. 40

6. Checkpoint 1a
How do we get E from V??
Look at slopes !!! 08

7. Checkpoint 1b A B C D
How do we get E from V??
Look at slopes !!! 08

8. Equipotentials
Equipotentials are the locus of points having the same potential.
Equipotentials produced by a point charge
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
Equipotentials are
ALWAYS
perpendicular to the electric field lines
The SPACING of the equipotentials indicates
The STRENGTH of the electric field 40

9. Checkpoint 3a A B C D 08

10. Checkpoint 3b A B C D 08

11. HINT
E - FIELD
LINES A B C D
EQUIPOTENTIALS
What is work done by E field to move negative charge from A to C ?
(A) WAC < (B) WAC = (C) WAC > 0 A B C D
A and C are on the same equipotential
WAC = 0
Equipotentials are perpendicular to the E field: No work is done along an equipotential. 08

12. Checkpoint 3b Again? A and C are on the same equipotential
B and D are on the same equipotential
Therefore the potential difference between A and B is the SAME as the potential between C and D 08

13. Checkpoint 3c A B C D A B C D 08

14. What is V(r) as a function of r?
cross-section a4 a3 +Q
Point charge q at center of concentric conducting spherical shells of radii a1, a2, a3, and a4. The inner shell is uncharged, but the outer shell carries charge Q.
What is V(r) as a function of r? a2 a1 +q
metal
metal
- Charges q and Q will create an E field throughout space
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
Spherical symmetry: Use Gauss’ Law to calculate E everywhere
Integrate E to get V 40

15. r > a4 : What is E(r)? (A) 0 (B) (C) (D) (E) +Q +q r Why?
Gauss’ law: r a4 a3 +Q
r > a4 : What is E(r)?
(A) (B) (C) a2 a1 +q
(D) (E)
metal
metal
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

16. a3 < r < a4 : What is E(r)?+Q
a3 < r < a4 : What is E(r)?
(A) (B) (C) r
Applying Gauss’ law, what is Qenclosed for red sphere shown?
(A) q (B) –q (C) 0 a2 a1 +q
(D) (E)
metal
metal
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
How is this possible???
-q must be induced at r=a3 surface
charge at r=a4 surface = Q+q

17. +q
metal +Q a1 a2 a3 a4
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

18. Just like a point charge !+q
metal +Q a1 a2 a3 a4
First find V(r) for r  a4
For r  a4
Just like a point charge !
So…

19. V( r ) constant inside a conductor !+q
metal +Q a1 a2 a3 a4
How about V(r) for ?
V( r ) constant inside a conductor !

20. +q
metal +Q a1 a2 a3 a4
V(r) for ?

21. +q
metal +Q a1 a2 a3 a4
V(r) for ?

22. +q
metal +Q a1 a2 a3 a4
V(r) for ?

23. Summary V a1 a2 a3 a4 r
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.