1. Electric Potential (III)
- Fields
Potential
Conductors

2. Potential and Continuous Charge Distributions
We can use two completely different methods:
Or, Find from Gauss’s Law, then…

3. Ex 1: Given V=3x2+12x-1, find where E=0.

4. Ex 2: The Electric Potential of a Dipoley a a x -q +q P
Find: a) Potential V at point P b) What if x>>a ? c) Find E.

5. Solution

6. Ex 3: Find the potential of a finite line charge at P,
AND the y-component of the electric field at P. P r d dq x L

7. Solution

8. Ex 3: Find the potential of a uniformly charged sphere of
radius R, inside and out. R

9. Uniformly Charged Sphere,radius RV r R

10. Recall that the electric field inside a solid conducting sphere
with charge Q on its surface is zero. Outside the sphere
the field is the same as the field of a point charge Q
(at the center of the sphere). The point charge is the
same as the total charge on the sphere.
Find the potential
inside and outside the sphere. +Q R

11. Solution
Inside (r<R), E=0, integral of zero = constant, so V=const
Outside (r>R), E is that of a point charge, integral gives
V=kQ/r

12. Solid Conducting Sphere,radius RV r R

13. Quiz
A charge +Q is placed on a spherical conducting shell. What is the potential (relative to infinity) at the centre? +Q
keQ/R1
keQ/R2
keQ/ (R1 - R2)
zero R1 R2

14. Calculating V from Sources:
Point source:
(note: V0 as r ) or
ii) Several point sources:
(Scalar)
iii) Continuous distribution:
OR … I. Find from Gauss’s Law (if possible)
II. Integrate, (a “line integral”)