Two thin wire rings each having a radius R are placed at a distance d apart with their axes coiciding. The charges on the two rings are `+q` and `-q`. The potential difference between the centres of the two rings is

Options

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

Answer

C

Explanation

`V_(1) = (q)/(4pi epsilon_(0)R) - (q)/(4pi epsilon_(0)sqrt(R^(2) + d^(2)))`
`V_(2) = -(q)/(4pi epsilon_(0)R) + (q)/(4pi epsilon_(0)sqrt(R^(2) + d^(2)))`
`V_(1) - V_(2) = (2q)/(4pi epsilon_(0))[(1)/(R ) - (1)/(sqrt(R^(2) + d^(2)))]`
`V_(1) - V_(2) = (q)/(2pi epsilon_(0))[(1)/(R ) - (1)/(sqrt(R^(2) + d^(2)))]`