Question

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?

Answer 1

Charge density of the long charged cylinder of length L and radius r is λ.

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.

Electric flux through the Gaussian surface is given by Gauss’s theorem as,

`phi = "E"(2pi"d")"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"(2pi"dL") = "q"/in_0`

Where,

q = Charge on the inner sphere of the outer cylinder

∈₀ = Permittivity of free space

`"E"(2pi"dL") = (lambda"L")/(in_0)`

`"E" = lambda/(2piin_0"d")`

Therefore, the electric field in the space between the two cylinders is E = `lambda/(2piin_0"d")`.