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Question

A current carrying loop is placed in a uniform magnetic field in four different orientations I, II, III and IV as shown in figure. Arrange them in decreasing order of potential energy.
639367_e4610900d2ed41e7be87a637f4b5765e.png

A
I > III > II > IV
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B
I > II > III > IV
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C
I > IV > II > III
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D
III > IV > I > II
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Solution

The correct option is C I > IV > II > III
As we know that, potential energy of a magnet in a magnetic field
U=mB
=mBcosθ
where, m= magnetic dipole moment of the magnet
B= magnetic field
Case I θ=180o
U1=mBcos180o
=mB [cos180o=1]
Case II θ=90o
U2=0 [cos90o=0]
Case III θ is acute angle
θ(0,90o)
cosθ= positive
Thus, U3= negative
Case IV θ is obtuse
θ(90o,180o)
cosθ(0,1)
Thus, U4= positive
Therefore, decreasing order of PE is
I > IV > II > III

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