A charge Q is distributed nonuniformly over a thin ring of r

A charge Q is distributed non-uniformly over a thin ring of radius R. A point charge q is brought from infinity to the center of the thin ring. Calculate the total work done by the electrostatic field forces in this process.

Solution

5)

Potential at centre of thin ring = kQ/R

where k = 1/4pi e0

Q = total charge on ring (independent whether distributed uniformly or non-uniformly)

R = radius of ring

final V = kQ/R

initial potential at infinity = 0

and work done = - q (deltaV) = - q ( kQ/R) = - kQq/R

Ans. KQq/R   or Qq / (4 pi e0 R)