By symmetry, the electric field must point radially outward from the wire at each point; that is, the field lines lie in planes perpendicular to the wire. In solving for the magnitude of the radial electric field E(r) produced by a line charge with charge density λ, one should use a cylindrical Gaussian surface whose axis is the line charge. The length of the cylindrical surface L should cancel out of the expression for E(r).
Apply Gauss's law to this situation to find an expression for E(r).
The concept of Gauss Law and charge density is applied to solve the problem.
Gauss law states that the total electric fields at any point on a closed gaussian surface is equal to the ratio of the net charge enclosed by that surface.
Mathematically from Gauss law ; EA = Q /ε.............equation1
from Linear charge density λ = Q/L
Q = λL = net charge enclosed
For cylindrical surface ; A = 2πrL = area
L = Length of charged object
E = electric field
plugging the expressions in equation1
E(r) x 2πrL = λL/ε
E(r) = λL/2πrLε which is the expression for the radial electric field
