Question

Two isolated conducting spheres are separated by a large distance. Sphere 1 has a radius of R and an initial charge 3Q while sphere 2 has a radius of 3R and an initial charge 7Q. A very thin copper wire is now connected to the spheres to allow charge to flow between the spheres. How much charge will be transferred from sphere 2 to sphere 1? (Note that the charge transferred can be positive, negative or zero.)

Answer 1

The requirement that the potential be constant on the conductors leads to the condition kQ1/R = kQ2/3R or Q2 = 3Q1. The total charge is 10Q, which from the constant potential condition must be split as Q1 = 2.5Q and Q2 = 7.5Q . Since the initial charge on sphere 1 is 3Q, the charge transferred to it must be −Q/2.