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Two identical thin ring, each of radius ...

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

A

zero

B

`(q(Q_1-Q_2)(sqrt2-1))/(4sqrt(2)piepsilon_0R)`

C

`(qsqrt(2)(Q_1+Q_2))/(4piepsilon_0R)`

D

`(q(Q_1+Q_2)(sqrt2+1))/(4sqrt(2)piepsilon_0R)`

Text Solution

Verified by Experts


the work done in moving a charge from A to B is
`W=(TPE)_(A)-(TPE)_(B)`
`TPE=` total potential energy
`(TPE)_(A)=[PE" due to "Q_(1)+PE" due to "Q_(2)]`
`=[((Q_(1))/(4piepsilon_(0)R))xxq+((Q)/(4piepsilon_(0)sqrt(R^(2)+R^(2))))q]`
`=(q)/(4piepsilon_(0)R)[Q_(1)+(Q_(2))/(sqrt(2))]`
`(TPE)_(B)[PE" due to "Q_(2)+PE" due to "Q_(2)]`
`=[((Q_(2))/(4piepsilon_(0)R))q+((Q_(1))/(4piepsilon_(0)sqrt(R^(2)+R^(2))))q]`
`=(q)/(4piepsilon_(0)R)[Q_(2)+(Q_(1))/(sqrt(2))]`
`thereforeW=(q)/(4piepsilon_(0)R)[Q_(1)(1-(1)/(sqrt(2)))-Q_(2)(1-(1)/(sqrt(2)))]`
`=(q(Q_(1)-Q_(2)))/(4piepsilon_(0)R)((sqrt(2)-1)/(sqrt(2)))`
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