CBSE Class 12-science Answered

A line charge is in the form of a thin charged rod with linear charge density λ. Let us find out an expression for electric intensity at any point P at a perpendicular distance r from the rod.

Let us consider a right circular closed cylinder of radius r and length l, with infinitely long line of charge as its axis.

The magnitude of electric field intensity at every point on the curved surface of the cylinder is same, because all such points are at the same distance from the line charge.

Contribution of curved surface of cylinder towards electric flux,

                                  ()

  Where   is the curved surface area of cylinder.

On the ends of the cylinder angle between and is 90. Therefore these ends make no contribution to the electric flux of the cylinder.

E ()

Charge enclosed in the cylinder= linear charge density x length = λl

According to Gauss's theorem

The direction of electric field vector will be the function of whether the line charge is positive or negative

If λ < 0, i.e., in a negatively charged wire, the direction of  is radially inward towards the wire.
If λ > 0, i.e., in a positively charged wire, the direction of  is radially out of the wire.