Question

A very long (nearly infinite) wire is made of an insulating material. The wire carries a charge, Q, which is distributed evenly along the entire length of the wire, giving it a uniform linear charge density, lambda. A Gaussian cylinder of length L and radius R is coaxial with the wire and encloses a portion of the charged wire. What is the charge enclosed by the Gaussian cylinder?

Answer 1

The cylinder is coaxial with the wire, therefore the wire runs through the center of the cylinder's circular faces. The cylinder has a length L, therefore it contains a length of wire L. Therefore the amount of charge inside a length of charged wire is given by:

Q = λL

where Q is the charge, λ is the wire's linear charge density, and L is the length of wire.