#### Question

A long charged cylinder of linear charged density λ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?

#### Solution

Charge density of the long charged cylinder of length *L* and radius *r* is *λ*.

Another cylinder of same length surrounds the pervious cylinder. The radius of this cylinder is *R*.

Let *E* be the electric field produced in the space between the two cylinders.

Electric flux through the Gaussian surface is given by Gauss’s theorem as,

`phi=E(2pid)L`

Where, *d *= Distance of a point from the common axis of the cylinders

Let *q* be the total charge on the cylinder.

It can be written as

`therefore phi=E(2pidL)=q/in_0`

Where,

*q* = Charge on the inner sphere of the outer cylinder

∈_{0} = Permittivity of free space

`E(2pidL)=(lambdaL)/(in_0)`

`E=lambda/(2piin_0d)`