# Electrostatic potential of two spheres

1. Jul 26, 2011

### pc2-brazil

1. The problem statement, all variables and given/known data
Two identical conducting spheres, with a radius of 15.0 cm, are separated by a distance of 10 m. What is the charge in each sphere, if the potential of one sphere is +1500 V, and the potential of the other one is -1500 V? Which assumptions did you make?

2. Relevant equations
Potential at the surface of a conductor with charge q and radius R:
$$V = \frac{q}{4\pi\epsilon_0R}$$

3. The attempt at a solution

If there was only one sphere at a potential of 1500 V, its charge would be:
$$q = 4\pi\epsilon_0RV = 4\pi(8.85\times 10^{-12})(0.15)(1500)=2.5\times 10^{-8} C$$
But I don't know how to account for the fact that there are two spheres. Also, to what exactly is it referring by saying that each sphere is at a particular potential? Is it the potential due to the whole system?

2. Jul 26, 2011

### EWH

Capacitance = Charge / Voltage
(The charge is for each sphere or plate, not both together)
See: http://en.wikipedia.org/wiki/Capacitance
and look at the table entry: "Two spheres,equal radius"

"Also, to what exactly is it referring by saying that each sphere is at a particular potential? Is it the potential due to the whole system?"
The voltages are relative to an arbitrary measurement point, say the earth, or a point equidistant between the spheres. In this case, the net charge is 0, one sphere has a deficit of charge and the other a surplus.

Last edited: Jul 26, 2011
3. Aug 1, 2011

### pc2-brazil

$$V = (1500)\frac{0.15}{10} = 22.5 V$$
$$q = 4\pi\epsilon_0 RV = 4\pi\epsilon_0 R(1500 + 22.5) = 2.54 \times 10^{-8}C$$