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Question:

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60º, and one of the fields has a magnitude of 1.2 x 10-2T. If the dipole comes to stable equilibrium at an angle of 15º with this field, what is the magnitude of the other field?

Answer:

Magnitude of one of the magnetic fields, B1= 1.2 × 10 - 2 T

Magnitude of the other magnetic field = B2

Angle between the two fields, θ= 60°

At stable equilibrium, the angle between the dipole and field B1, θ1= 15°

Angle between the dipole and field B2, θ2= θ - θ1 = 60° - 15° = 45°

At rotational equilibrium, the torques between both the fields must balance each other.

∴Torque due to field B1= Torque due to field B2

MB1sinθ1= MB2sinθ2 

Where, M= Magnetic moment of the dipole

Hence, the magnitude of the other magnetic field is 4.39 × 10 - 3T.


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