# Field of a Polarized Object

1. Oct 24, 2012

### KeyToMyFire

ρ1. The problem statement, all variables and given/known data

A sphere of radius a has a radial polarization P = krn$\hat{r}$ where k and n are constants and n $\geq$ 0.

a.) Find the volume and surface charge densities of bound charge.

b.) Find E outside and inside the sphere. Verify that you results for E satisfy the appropiate boundary conditions.

c.) Find V (potential) outside and inside the sphere.

d.) Sketch the results.

2. Relevant equations

σb = P $\cdot$ $\hat{n}$

ρb = -$\nabla$ $\cdot$ P

3. The attempt at a solution

I got

σb = krn

and

ρb = -(n+2)krn-1

which I'm pretty sure is right, but then for E I get

Einside = -krn$\hat{r}$0

which seems okay and then

Eoutside = 0

which doesn't seem right.

Can anybody tell if this is right or not? And if not how to do it?

Last edited: Oct 24, 2012
2. Oct 24, 2012

### TSny

I think everything is correct, except you need to specify a specific value of r in your expression for σb.

To see if it's reasonable that E = 0 outside the sphere, calculate the net charge of the sphere due to both the bound volume charge density and the bound surface charge density.

Last edited: Oct 24, 2012