Question 2.17:

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

 
The charge density of the long charged cylinder of length L and radius r is Another cylinder of the same length surrounds the previous cylinder. The radius of this cylinder is R.
Let E be the electric field produced in the space between the two cylinders.
The electric flux through the Gaussian surface is given by Gauss's theorem as, ϕ = E2πdL
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
ϕ = E2πdL = qε0Where, q Charge on the inner sphere Of the outer cylinder
ε0 = permittivity of free space
E(2πdL)=λLϵ0E=λ2πϵ0d
Therefore, the electric field in the space between the two cylinders is λ2πϵ0d