Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 19

In Example 3- 5 we obtained the electric field intensity around an infinitely long line charge of a uniform charge density in a very simple manner by applying Gauss's law. Since |E| is a function of r only, any coaxial cylinder around the infinite line charge is an equipotential surface. In practice, all conductors are of finite length. A firute line charge carrying a constant charge density l along the axis, however, does not produce a constant potential on a concentric cylindrical surface. Given the finite line charge l of length L in Fig., find the potential on the cylindrical surface of radius b as a function of x and plot it.
Figure: A finite line charge

( Hint: Find dV at P due to charge l dx' and integrate.)