An isolated system consists of two conducting spheres A and B. Sphere A has five times the radius of sphere B. Initially, the spheres are given equal amounts of positive charge and are isolated from each other. The two spheres are then connected by a conducting wire.
Note: The potential of a sphere of radius R that carries a charge Q is V = kQ/R, if the potential at infinity is zero.
-Determine the ratio of the charge on sphere A to that on sphere B, q_A/q_B, after the spheres are connected by the wire.

Question

Quizplus · Accepted Answer

When two conducting spheres are connected by a wire, they reach the same potential. Since sphere A has five times the radius of sphere B, the charge will distribute such that the potential V = kQ/R is equal for both. This results in q_A/q_B = R_A/R_B = 5/1 = 5.

An Isolated System Consists of Two Conducting Spheres a and B