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)(sqrt2-1))/(sqrt2(4piepsilon_0R))`
C. `(qsqrt2(Q_1+Q_2))/((4piepsilon_0R))`
D. `q(Q_1/Q_2)(sqrt2+1)sqrt2(4piepsilon_0R)`

Answer

B

Explanation

`V_(C_1)=V_(Q_1)+V_(Q_2)=1/(4piepsilon_0) Q_1/R+1/(4piepsilon_0) Q_2/(Rsqrt2)=1/(4piepsilon_0R) (Q_1+Q_2/sqrt2)`
Similarly `V_(C_2)1/(4piepsilon_0R) (Q_2+Q_1/sqrt2)`
`:. DeltaV=V_(C_1)-V_(C_2)`
`=1/(4piepsilon_0R)[(Q_1-Q_2)-1/sqrt2(Q_1-Q_2)]`
`=(Q_1-Q_2)/(sqrt2(4piepsilon_0R))(sqrt2-1)`
`W=q/_\V=q(Q_1-Q_2)(sqrt2-1)/sqrt2(4piepsilon_0R)`