Calculating Net Charge Using Electric Potential and Gauss' Law

[azone]

If we are given the formula for the electric potential V(r,theta) outside a spherical shell, how can we find the net charge on the shell? Essentially, I guess I'm a little confused about the relationship between Electric Potential and Net Charge.

The way I thought about this is by finding the electric field, which is the negative divergence of V. And if there is an electric field, this must mean that there is a a net charge that is not zero. But how can I find the magnitude of the charge? Or is there an easier way that I'm missing?

thanks

 

[Dick]

Take your electric field and apply Gauss' Law to a surface outside of the shell.