# Calculating potential on surface of sphere

1. Feb 12, 2012

### mm2424

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

A spherical drop of water carrying a charge of 30 pC has a potential of 500 V at its surface (which V = 0 at infinity). What is the radius of the drop?

2. Relevant equations

Potential = (1/4εpi) q/r

3. The attempt at a solution

When I first looked at this problem, I assumed that pure water would have charge evenly distributed, since it's not a conductor...and I was confused, because I wasn't sure how to calculate the charge on the surface, which is where the Voltage is given. To answer this problem, do we have to assume that the charge is located on the surface and then use the equation for potential? I did so, and got the right answer. However, I'm not sure whether I am right that we have to make this assumption, or whether there is some larger theoretical issue whereby it doesn't matter whether the charge is on the surface of evenly distributed throughout the sphere.

2. Feb 12, 2012

### SammyS

Staff Emeritus
What does Gauss's Law tell you about the E-field external to the drop. Does it matter whether the charge is distributed uniformly on the surface or distributed uniformly throughout the volume?