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

Explanation

Charge density of the long charged cylinder of length L and radius r is `lambda`. Another cylinder of same length surrounding the previous cylinder. The radius of the cylinder is R.
Let E be the E.F produced in the space between the two cylinders. electric flux. through the gaussian surface is given by gauss's theoram 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
`:. phi=E=(2pidL) =q/(in_(0))`
where, q=charge on the inner sphere of the outer cylinder
`in_(0)`=permitivity of free space
`E(2pidL)=(lambdaL)/(in_(0))`
`E=(lambda)/(2piin_(0)d)`
Therefore, the electric field in the space between the two cylinders is `(lambda)/(2piin_(0)d)`