A hollow cylinder of radius r and height h has a total charge q uniformly distributed over its surface. The axis of the cylinder coincides with the z axis, and the cylinder is centered at the origin, as shown in the figure.
What is the electric potential V at the origin?
The Attempt at a Solution
So, essentially, I'm attempting to derive the equation for electric potential at the origin of a cylinder. The problem first asks me to consider the cylinder as a series of rings and find the potential for a given ring. Once I have that, I should be able to integrate that expression to find the potential for the cylinder itself, but I'm having trouble even deriving the potential for a ring.
We are told that the charge of a ring is dq=qdz/h. Trying to understand this precisely, this means that the charge of a ring is equal to the charge at a given thickness along h? Please feel free to correct me if I'm wrong!
So given that that is our charge, we can now attempt to find the potential at the origin for a ring, and this is where I can't seem to derive the correct equation.
dV(z)=(1/4piε)∫dq/r = (1/4piε)∫qdzr/h = (1/4piε)qr/h∫dz
For this portion, it requests that the answer be in terms of dz, z, q, h, r, and epsilon_0, and I'm pretty sure I've already gone wrong somewhere, in terms of arriving at the solution.
If someone could please help me out, I'd really appreciate it.