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