`PQ` is an infinite current carrying conductor. `AB` and `CD` are smooth conducting rods on which a conductor `EF` moves with constant velocity `v` as shown. The force needed to maintain constant speed of `EF` is

Options

A. (a)`(1)/(VR)[(mu_(0)IV)/(2pi)1n((b)/(a))]^(2)`
B. (b)`[(mu_(0)IV)/(2pi)1n((b)/(a))]^(2)(1)/(VR)`
C. ( c)`[(mu_(0)IV)/(2pi)1n((b)/(a))]^(2)(V)/(R)`
D. (d)`(V)/(R)[(mu_(0)IV)/(2pi)1n((b)/(a))]^(2)`

Answer

A

Explanation

(a) i nduced emf `int_(a)^(b) BVdx = int_(a)^(b)(mu_(0)I)/(2pix)BVdx`
`rarr` Induced e.m.f. `= (mu_(0)IV)/(2pi)1n((b)/(a))`
Power dissipated `= (E^(2))/(R )`
Also, power `= FV rarr F = (E^(2))/(VR)`
`rarr F = (1)/(VR)[(mu_(0)IV)/(2pi)1n((b)/(a))]^(2)`