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PQ is an infinite current carrying condu...

`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

A

`(1)/(VR)[(mu_(0)IV)/(2pi)ln((b)/(a))]^(2)`

B

`[(mu_(0)IV)/(2pi)ln((b)/(a))]^(2) (1)/(VR)`

C

`[(mu_(0)IV)/(2pi)ln((b)/(a))]^(2) (V)/( R)`

D

`(V)/(R )[(mu_(0)IV)/(2pi)ln((b)/(a))]^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Induced emf `underset(a)overset(b)int BV dx = underset(a)overset(b)int(mu_(0)I)/(2pi x)BV dx`
`rArr` Induced e.m.f. `= (mu_(0)IV)/(2pi)In((b)/(a))`
`rArr` Power dissipated `= (E^(2))/(R )`
Also, power `= FV rArr F = (E^(2))/(VR)`
`rArr F = (1)/(VR)[(mu_(0)IV)/(2pi)In((b)/(a))]^(2)`
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