Rutgers Physics 385 Electromagnetism I (Fall15/Gershtein)

Homework 8 - Due November 5, 2015 in class

1) A perfect dipole p is situated a distance z above an infinite conducting grounded plane (see sketch below)

The dipole makes an angle Θ with the perpendicular to the plane.
Find the torque on p. If the dipole is free to rotate, in what orientation will it come to rest?

2) A sphere of radius R carries a polarization P(r) = kr , where k is a constant and r is the vector from the center.
a) calculate the biynd charges σb and ρb.
b) fine the field inside and outside the sphere

3) A thick spherical shell (inner radius a, outer radius b) is made out of dielectric material with "frozen-in" polarizaton
, where k is a constant and r is the distance from the center. There is no free charge in this problem.
Find the electric field in all three regions in r by two different methods:
a) Locate all the bound charges and use Gauss'es law for electric field;
b) Find D and then get E from D and P.