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Q.

A plane loop, shaped as two squares of sides a = 1 m and b =0.4 m is introduced into a uniform magnetic field⊥to the plane of loop (figure). The magnetic field varies as B=10-3 sin(100t) T. The amplitude of the current induced in the loop if its resistance per unit length is r=5mΩm−1 is

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a

2A

b

3A

c

4A

d

5A

answer is B.

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Detailed Solution

ϕ (flux linked)  =a2Bcos⁡0∘−b2Bcos⁡180∘ =a2−b2B E=−dϕdt=−a2−b2dBdt =a2−b2B0ωcos⁡ωt where B=B0,sin⁡ωt,B0=10−3T,ω=100∴ Imax=a2−b2B0ωR and R=(4a+4b)r=4(a+b)r∴ Imax=(a−b)B0ω4r=(1−0.4)×10−3×1004×5×10−3=3A
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