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Q.

A horizontal magnetic field B is produced across a narrow gap between the two square iron pole pieces. A closed square loop of side a, mass m and resistance R is allowed to fall with the top of the loop in the field. The loop attains a terminal velocity equals to

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a

B2a2Rmg

b

mgB2a2R

c

mgRB2a2

d

a2RmgB2

answer is A.

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Detailed Solution

Induced emf in the loop, when it is falling with terminal velocity e=BVa 

i=eR=BVaR

Vertically upward force experienced by loop due to this

F=Bia=BBVaRa=B2Va2R

When the loop attains terminal velocity ‘V’

mg=B2Va2R

V=mgRB2a2

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