Maximum potential given a charge

[c1223]

Homework Statement

So the question states that we have a hollow metal sphere of radius 2cm that is charged up. We take the breakdown field of air to be 1MV/m. We are asked to:

a) Calculate the maximum amount of charge which can be placed on the sphere.
b) Calculate the maximum potential on the surface of the sphere.

Homework Equations

$E = \frac{Q}{4\Piε_{0}r^{2}}$

The Attempt at a Solution

a) $1\cdot10^{6} = \frac{Q}{4\Piε_{0}0.02^{2}}$

So we get Q as being $4.4\cdot10^{-8}C$​

However, I'm stuck with what to do next to get the potential. I'm not entirely sure I understand the question? Is it the potential between that space on the surface and the center of the sphere?

I know the answer (or at least it is given as 20kV) but I'm not sure how to arrive at that answer.

Cheers

 

[c1223]

I think I might have cracked it. I realized that I also need the equation for potential which is:

$V = \frac{Q}{4\Piε_{0}r}$

Could someone please explain why it is $r^{2}$ for electric field but $r$ for potential?

 

[voko]

You just need to recall how the potential and the field are related to Coulomb's force.