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 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|

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

Solution

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

Solution

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

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):

Solution

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

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 .

+ - - + - conductor + - + -

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

Solution

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

Solution

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