Problem 35.

Initially, sphere A has a charge of -50e and a sphere B has a charge of +20e. The spheres are made of conducting material and are identical in size. If the spheres then touch, what is the resulting charge on sphere A?

Solution

In this problem we need to use two facts:

(1) the conservation of the net charge of the system of two spheres and

(2) the fact that the spheres are conducting, which means that the potentials of the spheres should be the same (at the moment when they touch each other). Since the spheres are identical in size then the fact that the potential of the spheres are the same means that the charges of the sphere (when the spheres are in contact) should be the same.

Therefore the final charge of sphere A is equal to the final charge of sphere B:

The conservation of the charge of the system of two spheres (this is an isolated system) means that the net initial charge of two spheres is equal to the net final charge:

We know the initial charges of the spheres, then