Does the potential of two spheres become equal when we connect them?

Question

I was reading a chapter on capacitors where it was asked whether given two spheres, each carrying a charge $q$ and of radius $r$ and $2r$, will charge flow between them?

I assume the answer should be no as both are having the same charge (that is what I learned in electrostatics that charge redistributes in such a way that charges become equal). But the book says that charge will flow. My friend told me that their potential will become equal. But why will their potential become equal (if it does)?

Answer 1

Whenever there is a Potential difference, there would be a flow if there is a conductor in place (like your case, where metal objects are in touch)

The flow will continue until the potential difference does not exist any more.

This is like water always flowing from a higher to lower altitude if it can. So across a metal, you will always have the same potential. Based on that you can calculate the charge for them.

It means, the charge in each sphere should be as much that the Potential on the surface (where they are in contact) would be equal for both objects. You also know the total charge in the system.This should be enough to solve the problem.

We know potential on surface of sphere equals kQ/R , so we have kQ1/R1 = kQ2/R2 or Q1/R2=Q2/R2. Also we know R1 is twice R2 and we know that Q1+Q2 equals 3. The rest is just simple math to figure out Q1 and Q2.

Answer 2

Q=CV , charge=capacitance times voltage , C is proportional to radius.

Thus the sphere with smaller radius will have smaller capacitance and larger potential. Charges will flow from the smaller sphere into the larger sphere until both have equal potentials.