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Question

A planar coil of area 7 m2 carrying an anti-clockwise current 2 A is placed in an extemal magnetic field B=(0.2^i+0.2^j0.3^k), such that the normal to the plane is along the line(3^i5^j+4^k). Select correct statements from the following . ( Consider Normal of the coil and Magnetic moment vectors to be in the same direction )

A
The potential energy of the coil in the given orientation is 6.4J
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B
The angle between the normal (positive) to the coil and the external magnetic field is cos1 (0.57)
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C
The potential energy of the coil in the given orientatlon is 3.2J
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D
The magnitude of magnetic moment of the coil is about 14 Am2
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Solution

The correct options are
C The potential energy of the coil in the given orientatlon is 3.2J
D The magnitude of magnetic moment of the coil is about 14 Am2
Area A=7m2, Normal ^n=150(3^i5^j+4^k)
17(3^i5^j+4^k)
area A=(3^i5^j+4^k)m2
Magnetic field B=(0.2^i+0.2^j0.3^k)T
Current I=2A
magnetic moment M=IA=(6^i10^j+8^k)Am2
|M|14Am2(2×7=14)
Potential energy U=M.B
=[1.222.4]=3.2J
Let θ be the angle between ^n and B(i.e.,)between M and B.
Now,U=MBcosθ.
cosθ=UMB=3.214×0.4(0.170.4)
=47=0.57
θ=πcos1(0.57)

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