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

Calculating E for symmetric charge distributions 1)Use symmetry to sketch the behaviour of E (possible only for very symmetric distributions) 2)Pick an imaginary “Gaussian surface” S 3)Calculate the flux through S, in terms of an unknown |E| 4)Calculate the charge enclosed by S from geometry 5)Relate 3) and 4) by Gauss’s Law, solve for |E|

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

Solution

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

Solution

Conductors (in Electrostatic Equilibrium) 1) inside a conductor. 2) just outside a conductor. 3)Any net charge on a conductor resides on the surface only.

Example: Hollow Thin Spherical Shell r r a P1P1 P2P2 Total charge Q Find E outside at P 1 : (r > a): Find E inside at P 2 : (r < a):

Solution

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

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

conductor

Surface Charge Density on a Conductor E = 0 inside dA 1 dA 2 E What is E at the surface of the conductor?

Solution

Example: Metal ball of radius R 1 has charge +Q Metal shell of radius R 2,and R 3 has total charge -3Q ) Find: charges on each surface. (and E) -3Q +Q R1R1 R2R2 R3R3

Solution

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