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

Options

A. `QR //4pi in_(0)d^(2)`
B. `Q/(2p in_(0))[ 1/R - 1/(sqrt(R^(2)+d^(2)))] `
C. zero
D. `Q/(4piin_(0))[1/R - 1/(sqrt(R^(2)+d^(2)))] `

Answer

B

Explanation

Potential at A due to both rings is
`V_(A) = (Kq)/R - (Kq)/(sqrt(R^(2)+d^(2)))" "...(a)`
Potential at B due to both rings is
`V_(B) = (K(-q))/R +(Kq)/(sqrt(R^(2)+d^(2)))`
`V_(A)-V_(B) = Q/(2piepsilon_(0)) [1/R = 1/(sqrt(R^(2)+d^(2)))]` .