Two fixed insulating rings A and B carry ahanges with uniform linear aharge density `+lambda` and `-lambda`, respectively, as shown in the adjacent figure. The planes of the rings are parallel to each other and their axes are coinciding. A particle of change "q" and mass "m" is released with zero velocity from centre P of the positively charged ring. The kinetic energy of the particle when it reaches centre Q of the negatively charge ring will be

Options

A. `sqrt((2lambdaq)/(m in_(0))(1 - (1)/(sqrt2))`
B. `(lambda)/(in_(0))(1 - (1)/(sqrt2))q`
C. `(lambda)/(2 in_(0))(1 - (1)/(sqrt2))q`
D. none of these

Answer

B

Explanation

Potential at P due to rings
`V_(P)=(lambda2piR)/(4piin_(0)R)-(lambda2piR)/(4piin_(0)sqrt2R)=(lambda)/(2in_(0))(1-(1)/(sqrt2))`
Potential at Q due to rings is
`V_(Q)=-(lambda)/(2in_(0))(1-(1)/(sqrt2))`
`Delta(K.E.)+(V_(Q)-V_(P))q=0`
`rArr (1)/(2)mv^(2)=(lambda)/(in_(0))(1-(1)/(sqrt2))q`