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?

Charge density of the long charged cylinder  of length L and radius r is λ .Another cylinder of same length surrounds the previous cylinder .The radius of the 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 ,

φ=E (2πd ) L

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

Let q be the total charge on the cylinder.

It can be written as

φ=E (2πdL ) = q/ε₀ 

Where ,q = Charge on the inner sphere of the outer cylinder

ε₀ = Permittivity of free space

E (2πdL) =λ L/ε₀

E= λ/2πε₀d

Therefore ,the electric field in the space between the two cylinders is λ/2πε₀d