Question

with necessary derivation prove that the electric field due to thin line charge is inversely proportional to the distance of observation point the line charge and is independent of its length ​

Answer 1

Answer:

Explanation:hii im not sure if its ur answer but i hope it helps:)

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.