Two circular loops of radii `0.05` and `0.09 m`, respectively, are put such that their axes coincide and their centers are `0.12 m` apart. A charge of `10^-6 C` is spread uniformly on each loop. Find the potential difference between the centers of the loops.

Options

A. `60KV`
B. `81KV`
C. `43KV`
D. `71 K V`

Answer

D

Explanation

The potential at the center of a ring will be due to charge on the rings, and as every element of a ring is a constant distance from the center, so
`V_1 (1)/(4 pi epsilon_0)[q_(1)/R_(1)+ q_(2)/sqrt(R_2^2 + x^2)]`
=`9 xx 10^9 [(10^-4)/(5) + (10^-4)/(sqrt(9^2 + 12^2))]`
=`9 xx 10^5 [(1)/(5) + (1)/(15)] = 2.40 xx 10^5 V`
Similarly,
`V_2 = (1)/(4 pi epsilon_0) [q_(2)/R_(2) + q_(1)/sqrt(R_1^2 + x^2)]`
.
or `V_2 = 9 xx 10^5 [(1)/(9) + (1)/(13)] = (198)/(117) xx 10^5 = 1.69 xx 10^5 V`
So `V_1 - V_2 = (2.40 - 1.69) xx 10^5 = 71 k V`.