# 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**) = k**r** ,
where *k* is a constant and **r** is the vector from the center.

a) calculate the biynd charges σ_{b} and ρ_{b}.

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**.