Q.

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4mm and a total length of 30 cm. The magnetic field changes with time at a steady rate dBdt=0.032Ts-1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23×10−8Ωm )

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a

0.34A

b

0.43A

c

0.61A

d

0.53A

answer is C.

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Detailed Solution

Flux=ϕ=Bℓ2cosθ       [Field is perpendicular to the loop. So, θ=00]Induced emf =ε=dB dtℓ2     [here ℓ=side of square ]Induced current =i=εR⇒i=dBdtℓ2(ρL)A    [here L=total perimeter of square, ℓ=L4]⇒i=dBdtLA16ρ⇒i=0.032×0.3×π×22×10-616×1.23×10-8=0.61 A
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A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4mm and a total length of 30 cm. The magnetic field changes with time at a steady rate dBdt=0.032Ts-1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23×10−8Ωm )