Question

A nonconducting ring of radius 0.5 m carries a total charge of 1.11 x 10^-10C distributed nonuniformly on its circumference, producing an electric field Vector E everywhere in space. The value of the line integral ∫  - Vector E. dl Vector dl l∈[l = ∞,l = 0](l = 0 being the centre of the ring) in volts is

(a) +2 

(b) -1 

(c) -2 

(d) 0

Answer 1

Correct Answer is: (a) +2

The line integral gives the work done in bringing a unit positive charge, on which the force is Vector E, from ∞ to the centre of the ring. This is equal to the potential at the centre, taking the potential at ∞ to be zero. Its value is V k = Q/R = 9 x 109 x 1.11 x 10^-10 / 0.5 = 2 V.