Solving Gaussian Charge Distribution Problem

Introduction to the Problem

A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of l, and the cylinder has a net charge per unit length of 2l. We need to use Gauss’s law to find:

1. (a) the charge per unit length on the inner surface of the cylinder
2. (b) the charge per unit length on the outer surface of the cylinder
3. (c) the electric field outside the cylinder a distance r from the axis

Answer

The detailed solution to this problem can be found in the attachment below. The application of Gauss law involves the use of imaginary surfaces and taking advantage of the symmetric properties of shapes.

Explanation

Using Gauss's law, we can solve this problem as follows:

1. The charge per unit length on the inner surface of the cylinder is -l.
2. The charge per unit length on the outer surface of the cylinder is 3l.
3. The electric field a distance r from the axis is (3l)/(2πεor) according to Gauss's Law.

A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of l, and the cylinder has a net charge per unit length of 2l. From this information, use Gauss’s law to find (a) the charge per unit length on the inner surface of the cylinder, (b) the charge per unit length on the outer surface of the cylinder, and (c) the electric field outside the cylinder a distance r from the axis.

The charge per unit length on the inner surface of the cylinder is -l, the outer surface is 3l, and the electric field a distance r from the axis is (3l)/(2πεor) according to Gauss's Law.