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

Magnitude of one of the magnetic fields (B1) = 1.2 × 10–2 T


The angle between the magnetic field directions (θ) = 60°


The angle between the dipole and the magnetic field B1 is θ1 = 15°


Let magnitude of second of the magnetic fields = B2


∴ The angle between the dipole and the magnetic field B2 is θ2 = θ-θ1 = 45°


Let magnetic moment of the dipole be M


Thus, at rotational equilibrium,


Torque due to field B1 = Torque due to field B2


⇒ M × B1sinθ1 = M × B2 sinθ2


⇒



⇒ B2 = 9 × 10-3 T


Thus, the magnitude of the other magnetic field = 4.39 × 10-3T


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