Question

Calculate the electric field a distance r from a line of electric charge infinite in extent with linear charge density λ.

Answer 1

Given

line of charge (wire) infinite length with linear charge density is λ

let us consider the line of charge is of positive and the field lines are radially out ward and uniform through out the length  

and the symmetry here is the cylindrical symmetry

from Gauss law ,

E*A cos theta = Q_in/

here theta = 0 because the field lines are perpendicular to the curved surface of the gaussian surface so cos 0=1

from the relation Lambda = Q/l ==> = Q = λ*l

so constructing a Gaussian surface of radius r , calculating the area A = 2pi*r*l , then

E = λ*l/(2pi*r*l*)

E = λ/(2pi**r)

the electric field a distance r from a line of electric charge infinite in extent with linear charge density λ is E = λ/(2pi**r)