Answer to Question #106137 in Electricity and Magnetism for Mukelo Madolo

Question

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 density,and the cylinder has a net charge per unit length of2density from this information use the 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.

Answer 1

a) Wire induces the inner surface of cylinder:

$$q_{in}=-\lambda L$$

b)

$$q_{cylinder}=q_{in}+q_{out}$$

$$2\lambda L=q_{out}-\lambda L$$

$$q_{out}=3\lambda L$$

c)

$$E(2\pi r L)=\frac{3\lambda L}{\epsilon_0}$$

$$E=\frac{3\lambda }{2\pi r \epsilon_0}$$

$$E=\frac{6k\lambda }{r}$$