Two thin wire rings each having radius R are placed at distance d apart with their axes coinciding. The charges on the two are `+Q` and `-Q`. The potential difference between the centre so the two rings is

Options

A. Zero
B. `(q)/(4pi epsilon_(0)) [(1)/(R ) - (1)/(sqrt(R^(2) + d^(2)))]`
C. `qR//4pi epsilon_(0)d^(2)`
D. `(q)/(2pi epsilon_(0)) [(1)/(R ) - (1)/(sqrt(R^(2) + d^(2)))]`

Answer

D

Explanation

Potentials at the centre of ring are

`V_(0_1) = (k.q)/(R ) + (k(-q))/(sqrt(R^(2) +d^(2))),V_(0_(2)) = (k(-q))/(R ) + (kq)/(sqrt(R^(2) +d^(2)))`
`rArr V_(0_(1)) - V_(0_(2)) = 2kq [(1)/(R ) - (1)/(sqrt(R^(2) +d^(2)))]`
`= [(1)/(R)- (1)/(sqrt(R^(2) +d^(2)))]`