Problem 20.

A cylinder with radius r= 0.75 m and length l=0.6 m that has an infinite line of positive charge running along its axis.  The charge per unit length on the line is .

(a) What is the electric flux through the cylinder due to this line of charge?

(b) What is the flux through the cylinder if its radius increased to r= 0.32 m?

(c) What is the flux through the cylinder if its length increased to l= 0.8 m?

Solution

From Gauss's law the flux through the surface depends only on the charge inside of this surface.

where

(a) The charge inside of the cylinder depends only on the length of the cylinder. It is

Then

(b) The charge inside of the cylinder depends only on the length of the cylinder, so in this case the charge is the same as in case (a). So the flux will be the same:

(c) Now the length is 0.8 m. Then

Then