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Q.

Current I flows through the circuit, as shown in figure. Find the magnetic moment of the figure, if AB = BC = CD = DE= EF = FG=GH=HA.

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a

72Iπa2

b

52Iπa2

c

4Iπa2

d

53Iπa2

answer is B.

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Detailed Solution

Angle θ for one segment, θ=2π8=π4 M0=IA=IA=Ir2θ2-r12θ2 =I(2a)2θ2-a2θ2=I·3a2θ2  For 4 segments, M=4I·3a2θ2=6Ia2θ  Magnetic moment due to circle =Iπa2  Total magnetic moment =6Ia2θ+Iπa2 =6Ia2×π4+I·πa2=52Iπa2
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