Two identical thin ring, each of radius R meters, are coaxially placed a distance R metres apart. If `Q_1` coulomb, and `Q_2` coulomb, are repectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is

Options

A. zero
B. `(q(Q_(1)-Q_(2))(sqrt(2)-1))/(sqrt(2).4piepsilon_(0)R)`
C. `(qsqrt(2)(Q_(1)+Q_(2)))/(4pi epsilon_(0)R)`
D. `(q(Q_(1)+Q_(2))(sqrt(2)+1))/(sqrt(2).4piepsilon_(0)R)`

Answer

B

Explanation

Work done `W_(21)=(V_(1)+V_(2))q`
`V=1/(4 pi epsilon_(0))[(Q_(1))/r+(Q_(2))/(sqrt(2)R)]` and `V_(2)=1/(4 pi epsilon_(0))[(Q_(2))/R+(Q_(1))/(sqrt(2)R)]`
Thus `W_(21)=(q(Q_(1)-Q_(2))(sqrt(2)-1))/(sqrt(2).4piepsilon_(0)R)`