# Dipole moment of polarized sphere

1. Dec 3, 2012

### SallyBieber

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

Consider a polarised sphere of radius R the polarization is given by
P vector = (ar^2 + b) r hat = ( ar+ b/r) r vector
Where a and b are constant

2. Relevant equations

Find the dipole moment of the sphere

3. The attempt at a solution

I knew that P (polarized)= delta p / delta volume
So to find dipole moment
I'll take : delta p = $\int p . dv$
I have a solution manual written in it that
P.r vector = Q
So the delta p = Q/4 pi r^2
How they got this equ.
Should i use the polarized equ. That given
Im so confused

Help

Last edited: Dec 4, 2012
2. Dec 3, 2012

### SallyBieber

Is here anyone can help!,,

3. Dec 4, 2012

### TSny

I don't think you need to do any calculation here.

Note that the polarization vector P has a direction that is radially outward at each point of the sphere and the magnitude of P depends only on r.

So, if you consider a small element of volume dV1 at some point in the sphere at a distance r from the center, the dipole moment of that element will be dp1 = P1dV1.

Now consider a second volume element dV2 (same size as dV1) that is at the same distance r from the center but is on the opposite side of the center from dV1. The dipole moment of that element will be dp2 = P2dV2.

How do the magnitudes of dp1 and dp2 compare? How do their directions compare?

What would you get if you add them: dp1 + dp2 = ?