Intensity of the electric field due to uniformly distributed charge on a wire of infinite length.
Or,
Intensity of the electric field near a uniformly charged straight wire of infinite length.
Suppose a charge is uniformly distributed on a line of length l.
If linear density of the distributed charge is λ,
Then the linear density is,
λ=q/l
Suppose there is a point p at a distance r from the wire, where the electric field intensity is to be found.
To find the electric field intensity at point P, draw a Gaussian cylindrical surface of radius r and length l.
Thus, the electric flux passing through the area element dA of the Gaussian surface.
dΦₑ = →E.→dA
dΦₑ = E.dA.Cosθ
dΦₑ = E.dA
Or,
Total electric flux passing through Gaussian surface,
Φₑ= ∫ₐE.dA
Φₑ= E ∫ₐdA
q/∈₀ = E(2πrl)
E= q/(2π∈₀rl)
E= λ/2π∈₀r [ λ=q/l ]
Similarly,
Electric field intensity E due to a linear charge is inversely proportional to the distance r from the point of linear charge.