# Electrostatic potential of two spheres

## Homework Statement

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?

## Homework Equations

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

## 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?

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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:
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.
But I'm looking for a solution that doesn't involve capacitance, since I found this question in a chapter that comes before the chapter on capacitance.
I found the following solution on the Internet: it assumes first that there is only one sphere at a potential of 1500 V, and calculates its charge as:
q = 2.5 × 10−8 C
like I did in the original topic.
Then it calculates the potential of this sphere at a distance of 10 meters:
$$V = (1500)\frac{0.15}{10} = 22.5 V$$
Then it says that it is small compared to 1500 V, so we can treat it as a perturbation, so that we can assume both spheres have a charge of:
$$q = 4\pi\epsilon_0 RV = 4\pi\epsilon_0 R(1500 + 22.5) = 2.54 \times 10^{-8}C$$
But I don't understand this final part. Why is it summing (1500 + 22.5)? Shouldn't it be (1500 - 22.5), since both spheres have opposite potentials?