1. Thin sheet of any charge distribution
tiny disk
Just to right of disk
Just to left of disk

2. Charges and fields of a conductor
In electrostatic equilibrium, charges inside a conductor do not move. Thus, E = 0 everywhere in the interior of a conductor.
Since E = 0 inside, there are no net charges anywhere in the interior. Net charges can only be on the surface(s).
The electric field must be perpendicular to the surface just outside a conductor, since, otherwise, there would be currents flowing along the surface.

3. Electrostatic Shielding (Continued)
If you move charge q in the cavity, the exterior electric fields and the extreior charge distribution are not affected. q
Conducting shell electrostatically shields its exterior from changes on the inside.
Add Q’
If you now add charge Q’ to the conductor and/or Q’’ on the outside of the conductor, the interior electric fields do not change.
Q’’ +
Conducting shell electrostatically shields its interior from changes on the outside, too.

4. READING QUIZ 1
IN WHAT DIRECTION CAN YOU MOVE A TEST CHARGE RELATIVE TO AN ELECTRIC FIELD SO THAT THE ELECTRIC POTENTIAL DOES NOT CHANGE?
A| Move in the direction of the electric field lines.
B| Move opposite to the direction of the electric field lines.
C| Move from point A in the electric field to point B in
in the electric field along an arbitrary path.
D| Move relative to the electric field along a path which is
everywhere perpendicular to the electric field.

5. Electric Potential Energy of a Charge in Electric Field
Coulomb force is conservative
=> Work done by the Coulomb force is path independent.
Can associate potential energy
to charge q0 at any point r in space.
It’s energy! A scalar measured in J (Joules)

6. Electric Potential Energy of a Charge (continued)
i is “the” reference point. Choice of reference point (or point of zero potential energy) is arbitrary.
i is often chosen to be infinitely far away (∞)

7. Gravitational vs Electrostatic Potential Energyb
Gravity
Coulomb
(if g, E uniform)
Work done by gravity or the Coulomb force decreases the potential energy.

8. Potential Energy in the Field due to a Point Charge q
From ∞
The potential drops along a field line!
This is also called the potential energy of the two-charge configuration of q and q0.
What is the work required to bring q0 in from infinity?

9. Potential Energy of a Multiple-Charge Configuration
(b)
(c)

10. Physics 241 –Warm-up quiz
Three point charges carry the same charge -q. Which of the following statements is true? Select one of (a) – (e). A B -q
An electron would have a higher potential energy at point A than at point B
A proton would have a higher potential energy at point A than at point B
An electron would have a lower potential energy at point A than at point B
The potential energy is the same for an electron and a proton at point A.
The potential energy is the same for a proton at point A and point B.

11. Scalar! Electric Potential
U(r) of a test charge q0 in electric field generated by other source charges is proportional to q0 .
So U(r)/q0 is independent of q0, allowing us to introduce electric potential V independent of q0.
taking the same reference point
[Electric potential] = [energy]/[charge]
SI units: J/C = V (volts)
A positively charged particle produces a positive electric potential; a negatively charged particle produces a negative electric potential.
Scalar!
Potential energy difference when 1 C of charge is moved between points of potential difference 1 V

12. Potential at P due to a point charge q
From ∞
The potential drops along a field line!

13. POTENTIAL DIFFERENCES V2 – V1
Electron Volt
V=U/q is measured in volts => 1 V (volt) = 1 J / 1 C
POTENTIAL DIFFERENCES V2 – V1
(electron volt)
V depends on an arbitrary choice of the reference point.
V is independent of a test charge with which to measure it.

14. Potential due to two (source) charges

15. Potential due to Multiple Source Charges: Example
Dotted line is an equipotential when
q1=12nC, q2= -24nC, q3=31nC, q4=17nC

16. Lecture 6-16
E from V
We can obtain the electric field E from the potential V by inverting the integral that computes V from E:
Expressed as a vector, E is the negative gradient of V

17. Lightning
E = 3 x 106 N/C
at electrical breakdown of air
ΔV on the order of 109 V

18. DOCCAM A-16 PROOF PLANE

19. Examples (only a Preview)
Point charge Q:
Uniformly charged sphere:
r > R
r < R
Charged disk:
Charged sheet:
Charged line:

20. Physics 241 – 10:30 Quiz 3 September 8, 2011
A spherical shell is uniformly charged with a positive charge density σ. Which of the following statements is (are) true? Select one of (a) – (e).
An electron would have a higher potential energy at point A than at point B
A proton would have a higher potential energy at point A than at point B
The electric potential is lower at A than at B
The electric potential is higher at A than at B
1 and 3 only
1 and 4 only
2 and 3 only
2 and 4 only
None of them σ A B

21. Physics 241 – 11:30 Quiz 3 September 8, 2011
A sphere is uniformly charged with a negative charge density. Which of the following statements is (are) true? Select one of (a) – (e).
A proton would have a higher potential energy at point A than at point B
An electron would have a higher potential energy at point A than at point B
The electric potential is lower at A than at B
The electric potential is higher at A than at B
1 and 3 only
1 and 4 only
2 and 3 only
2 and 4 only
None of them -σ A B

22. Physics 241 – 10:30 Quiz 3 January 27, 2011
A sphere is uniformly charged with a negative charge density. Which of the following statements is (are) true? Select one of (a) – (e).
A proton would have a higher potential energy at point A than at point B
An electron would have a higher potential energy at point A than at point B
The electric potential is lower at A than at B
The electric potential is higher at A than at B
1 and 3 only
1 and 4 only
2 and 3 only
2 and 4 only
None of them
+3σ A B

23. Physics 241 – 11:30 Quiz 3 January 27, 2011
A sphere is uniformly charged with a positive surface charge density. Which of the following statements is (are) true? Select one of (a) – (e).
A proton would have a higher potential energy at point A than at point B
An electron would have a higher potential energy at point A than at point B
The electric potential is lower at A than at B
The electric potential is higher at A than at B
1 and 3 only
1 and 4 only
2 and 3 only
2 and 4 only
None of them
+3σ A B