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Q.

A wire of cross-sectional area A forms three sides of a square and is free to rotate about axis OO1 . If the structure is deflected by an angle θ from the vertical when current  i is passed through it in a magnetic field B acting vertically upwards and density of the wire is ρ , then the value of θ is given by

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a

2AρgiB=cotθ

b

2AρgiB=tanθ

c

AρgiB=sinθ

d

Aρg2iB=cosθ

answer is A.

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Detailed Solution

Let  a is the side of square.Torque of current =   MB=sin(90−θ)=MBcosθ=ia2BcosθMass of each side=  m=ρAaTorque of gravity =  2mga2sinθ+mg a sinθ =2mg a sinθ=2ρAga2sinθNow, at equilibrium both torques should be samei.e.,  ia2Bcosθ=2ρAga2sinθ⇒ cotθ=2ρAgiB .
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