# Radii of eqiuipotential surfaces of a charged metal sphere

1. Feb 5, 2013

### RoosterCancer

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

A metal sphere of radius r0 = 0.29 m carries a charge Q = 0.90 µC. Equipotential surfaces are to be drawn for 100 V intervals outside the sphere. Determine the radius r of the following equipotentials from the surface.
a) first:___m
b) tenth:___m
c) 100th:_____m

2. Relevant equations

V=kQ/r --> r=kQ/V

3. The attempt at a solution

I've tried plugging the numbers from the problem in the equation:

r=(8.99 x 10^9 NM^2/C^2)*(0.9 x 10^-6 C)/(100V) = 80.91m

and it's incorrect. I assume the radius of the sphere itself comes into play, but I'm not sure where. Can anyone help?

2. Feb 5, 2013

### SammyS

Staff Emeritus
What is the potential at the surface of the ball ?

3. Feb 5, 2013

### RoosterCancer

I was able to find the potential of the ball:

V=(9 x10^9NM^2/C^2)*(0.9 x10^-6 C)/0.29m = 27931.03V

and was able to answer part a, by adding 100 V to the ball's potential and using the formula. So, for b, I added 1000 V to the potential and for c I added 10000 V to the potential, but the results were incorrect.