Mastering Physics Solutions: Potential of a Charged Cylinder

Potential of a Charged Cylinder

Part A = V = 1/(2πε0h) * ln(h/(2r) + sqrt(1 + (h^2 / (4r^2)))
Part B = V0 = q / (4πε0r)

Solutions Below:

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.

Part A

What is the electric potential V at the origin?

V = 1/(2πε0h) * ln(h/(2r) + sqrt(1 + (h^2 / (4r^2)))

Part B

What is the potential V0 in the limit as h goes to zero?

V0 = q / (4πε0r)

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