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Questions  

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(neglect the weight of conductor)

a
1vRμ0Iv2πln⁡ba2
b
μ0Iv2πln⁡ba 1vR
c
μ0Iv2πln⁡ba2vR
d
vRμ0Iv2πln⁡ba2

detailed solution

Correct option is A

Induced emf ∫ab Bvdx=∫ab μ0I2πxvdx⇒  Induced emf, E=μ0Iv2πln⁡ba⇒  Power dissipated =E2R Also, power =F⋅v⇒F=E2vRF=μ0Iv2πln⁡ba21vR

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