A non-conducting ring of radius r has charge per unit length `lambda`. A magnetic field perpendicular to plane of the ring changes at rate Db/dt. Torque experienced by the ring is

Options

A. `lambdapir^(3)(dB)/(dt)`
B. `lambda2pir^(3)(dB)/(dt)`
C. `lambda^(2)(2pir)^(2)(dB)/(dt)`
D. zero

Answer

A

Explanation

`e= (dphi)/(dt)= pir^(2)(dB)/(dt)rArr E(2 pi r) = pir^(2)(dB)/(dt)`
`E= (1)/(2) r (dB)/(dt)rArr dF = lambdadSE`
`rArr " "d tau= rlambdaDSE rArr tau = lambdarEintdS = lambdarE2 pi r`