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

Answer

B

Explanation

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