A long straight wire is surrounded by a hollow metal cylinde

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 and the cylinder has a net charge per unit length of 2. From this information, use Gauss\'s law to find the following. (Use lambda for epsilon-0 for 0, and r for r as necessary.) (a) the charge per unit length on the inner and outer surfaces of the cylinder (inner surface) (outer surface) (b) the electric field outside the cylinder, a distance r from the axis Submit AnswerSave Progress

Solution

The charge on inner surface of cyclinder = - lambda

The charge on outer surface of cyclinder = 2 lambda + lambda = 3 lambda

The electric field outside the cylinder, a distance r from the axis

From Guass law

phi * E .da = Q / epsilon₀

phi * E .da = | E | * 2 pi * r * l

Q = 3 lambda * l

| E | * 2 pi * r * l = 3 lambda * l / epsilon₀

so, Electric field outside cyclinder = 3 lambda / [2 pi * epsilon₀ * r]