Potential of hollow open ended cylinder

[FS98]

Homework Statement

A hollow circular cylinder, of radius a and length b, with open ends, has a total charge Q uniformly distributed over its surface. What is the difference in potential between a point on the axis at one end and the midpoint of the axis? Show by sketching some field lines how you think the field of this thing ought to look.

Homework Equations

The Attempt at a Solution

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I’m pretty sure I have to get the potential at one end of the open ended cylinder and then subtract the potential at the middle. I think the potential at the center is 0 because of symmerty, so the only think I have to find is the potential at one end. I’m not sure what equation to use for this though.

 

[gneill]

Perhaps you should start with the potential on the axis of a circular ring of charge, then think integration to "build up" your cylinder You've probably seen the result for the ring of charge, either in class or in your study materials. What is the formula?