A hollow, thin-walled insulating cylinder of radius R and length L (like the cardboard tube in a roll of toilet paper) has charge Q uniformly distributed over its surface.
Calculate the electric potential at any point x along the axis of the tube. Take the origin to be at the center of the tube, and take the potential to be zero at infinity.
Show that if L \ll R, the result of part A reduces to the potential on the axis of a ring of charge of radius R.
Use the result of part A to find the electric field at any point x along the axis of the tube.
Calculate the electric potential at any point x along the axis of the tube. Take the origin to be at the center of the tube, and take the potential to be zero at infinity.
Show that if L \ll R, the result of part A reduces to the potential on the axis of a ring of charge of radius R.
Use the result of part A to find the electric field at any point x along the axis of the tube.