Question

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?

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 sin θ₁ = MB₂ sin θ₂

Where,

M = Magnetic moment of the dipole

∴ B₂ = `("B"_1 sin θ_1)/(sin θ_2)`

= `(1.2 xx 10^-2 xx sin 15°)/(sin 45°)`

= 4.39 × 10⁻³ T

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