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))/((4sqrt(2)pi in_(0)R))`
C. `(qsqrt(2)(Q_(1)+Q_(2)))/(4pi in_(0)R)`
D. `(q(Q_(1)-Q_(2))(sqrt(2)+1))/((4sqrt(2)pi in_(0)R))`

Answer

B

Explanation

`U_(i)=(KQ_(1)q)/(R)+(KQ_(2)q)/sqrt(R^(2)+R^(2))`
`U_(f)=(KQ_(1)q)/sqrt(R^(2)+R^(2))+(KQ_(2)q)/(R)`
Work done by external force : `DeltaU=U_(f)-U_(i)`