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?

Given,

Charge density of the long-charged cylinder of length L and radius r is λ. Another same type of cylinder with radius R surrounded it.

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

Electric flux through a Gaussian surface is given by the Gaussian theorem as,

Φ = E(2πd)L

Where, d = distance of a point from common axis of the cylinders.

Let q be the total charge on the cylinder,

∴ Φ = E(2πd)L =

Where, q = charge of the inner sphere of the outer cylinder

ϵ₀ = permittivity of space

Thus,

E(2πd)L =

∴

Hence, the electric field between cylinders,