# Monopole Moment of a sphere of charge

1. Feb 15, 2008

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

I'm really bad at these type of problems. I'm supposed to find the monopole moment of this continuous charge distribution. its charge is

$$\sigma = const*cos(\theta)$$

2. Relevant equations

$$p = \int r'\rho(r')d\tau$$
which then since we are doing a surface charge should be
$$p = \int r' \sigma da$$

3. The attempt at a solution
Well, I want to do the double integral of something to find the charge distribution so I can find the monopole moment. I'm thinking something like
$$p = \int_{0}^{2 \pi}\int_{0}^{2 \pi} r' * c \cdot cos(\theta) sin( \theta) r^2 d\phi d\theta$$
and I'm thinking that r' is just r so then it would be

$$p = \int_0^{2\pi} d\phi \int_0^{\pi} r'^3cose(\theta)sin(\theta)d\theta$$

Last edited: Feb 15, 2008
2. Feb 15, 2008

The obvious problem that then comes up is that then appears is that I get a 0 term from the second integral that makes my whole monopole moment zero. Is this correct?

3. Feb 15, 2008

### captain

if you are supposed to calculate the monopole moment then you integrate the charge density only. the formulas you have above are those for a dipole moment. monopole moment is just total charge

4. Feb 15, 2008

### pam

The monopole moment is zero. Some of your formulas are wrong, as Capt. pointed out.

5. Feb 15, 2008