Question

A thin straight infinitely long conducting wire of linear charge density λ is enclosed by a cylindrical surface of radius r and length l. Its axis coinciding with the length of the wire Obtain the expression for the electric field, indicating its direction, at a point on the surface of the cylinder.

Answer 1

Electric field intensity due to an infinitely long uniformly charged wire at point P at distance r from it is obtained as follows:

Consider a thin cylindrical Gaussian surface S with charged wire on it axis and point P on its surface, then net electric flux through surface S is 

Φ = O+EA +0 or Φ = E.2πrl

But by Gauss’s theorem,

Φ =q/ε₀ = λl/ε₀

where q is the charge on length l of wire enclosed by cylindrical surface S and is uniform linear charge density of wire.

Thus, electric field of a line charge is inversely proportional to distance directed normal to the surface of charged wire.