1. Gauss’s Law (II) Examples: charged spherical shell, infinite plane,
long straight wire
Review: For a closed surface S:
Net outward flux through S

2. Calculating E for symmetric charge distributions
Use symmetry to sketch the behaviour of E (possible only for very symmetric distributions)
Pick an imaginary “Gaussian surface” S
Calculate the flux through S, in terms of an unknown |E|
Calculate the charge enclosed by S from geometry
Relate 3) and 4) by Gauss’s Law, solve for |E|

3. Example: Uniformly-Charged Thin Sheet+ + + + + + + + + + +
Gaussian surface
Find E due to an infinite charged sheet

4. Solution

5. Example: Infinite Line Charge (Long thin Wire)+ + + + + + + + + L
Find E at distance r from the wire

6. Solution

7. Conductors (in Electrostatic Equilibrium)
inside a conductor.
just outside a conductor.
Any net charge on a conductor resides on the surface only.

8. Example: Hollow Thin Spherical Shell+ +
Total charge Q + P1 + + r a + + r + + P2 + + + +
Find E outside at P1 : (r > a):
Find E inside at P2 : (r < a):

9. Solution

10. E=0 inside Consequences if E was not zero:
1) If , charges would move!!!
2) If , charges would move!!! E
Ell +
E=0 inside

11. 3) inside, so any Gaussian surface inside
3) inside, so any Gaussian surface inside the conductor encloses zero net charge. + + + + + + + + + + + + + + + + + + + + + + + + + + + +
So net charge =0
Since E = 0 everywhere .

12. + - - + -
conductor + - + -

13. Surface Charge Density on a Conductor
dA1
dA2 + + + + +
E = 0 inside
What is E at the surface of the conductor?

14. Solution

15. Example:
Metal ball of radius R1 has charge +Q
Metal shell of radius R2,and R3 has total charge -3Q )
Find: charges on each surface. (and E) R3 +Q R1 R2
-3Q

16. Solution

17. Quick Recap At surface of conductor Conductor:
Infinite Sheet of charge:
Why is the lower value half of the upper?