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.