Dipole moment of non-conducting spherical shell

[jackxxny]

Homework Statement

I'm trying to find the dipole moment of

The surface charge distribution is:

$$\sigma = \sigma_{0} sin 2 \theta$$

Homework Equations

The Attempt at a Solution

$$p_z=\int_{0}^{\pi}{\sigma* z* dA } = \int_{0}^{\pi}{(\sigma_0 \sin{2 \theta})*(acos{\theta})*(2\pi a^2 \sin{\theta}d\theta)}$$

Doing so I obtain

$$( \sigma_{0} a^3 \pi^2)/(2)$$

Can that be the answer?

 

[gabbagabbahey]

You should also explicitly show (or give a good argument for why) $p_x=p_y=0$ and then write your final answer in vector form (since dipole moment is a vector!) as $\textbf{p}=\frac{\sigma_{0} a^3 \pi^2}{2}\mathbf{\hat{z}}$, but other than that it looks good to me!