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 × 10⁻² T. If the dipole comes to stable equilibrium at an angle of 15º with this field, what is the magnitude of the other field?

Answer 1

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
MB₁ sinθ1 = MB₂ sinθ₂
Where,
M = Magnetic moment of the dipole

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