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Question

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle, of 75. One of the fields has a magnitude of 2×102T. The dipole attains stable equilibrium at an angle of 30 with this field. What is the magnitude of the other field?


A

0.01 T

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B

0.02 T

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C

0.03 T

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D

0.04 T

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Solution

The correct option is A

0.01 T


Refer to Fig. Let θ1 (=30) be the angle between the magnetic moment vector m and the field vector B1(=1.5×102T). Then, as shown in Fig. the angle between m and the other field B2 will be θ2=7530=45
The field B1 exerts a torque τ1=m×B1 on the dipole and the field B2 exerts a torque τ2=m×B2, where m in the magnetic moment of the dipole. Since the dipole is in stable equilibrium, the net torque τ(=τ1+τ2) must be zero, i.e. the two torques must be equal and opposite. In terms of magnitudes, we have mB1 sin θ1=mB2 sin θ2
or B2=B1 sin θ1sin θ2=2×102×sin 30sin 45=0.01 T


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