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 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, ϕ=E(2πd)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 ∴ϕ=E(2πdL)=∈0q Where, q= Charge on the inner sphere of the outer cylinder ∈0= Permittivity of free space E(2πdL)=∈0λL E=2π∈0dλ Therefore, the electric field in the space between the two cylinders is 2π∈0dλ.
