5.21 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 field, ${\mathrm{B}}_{\mathit{1}}=1.2×{10}^{\mathit{-}\mathit{2}}\mathrm{T}$
Magnitude of the other magnetic field, ${\mathrm{B}}_{2}$
Angle between the two fields, $\mathrm{\theta }=60°$
At stable equilibrium, the angle between the dipole and field
Angle between the dipole and field
|At rotational equilibrium, the torques between both the field
must balance each other.

${\mathrm{MB}}_{1}{\mathrm{sin\theta }}_{1}={\mathrm{MB}}_{2}{\mathrm{sin\theta }}_{2}$
$\mathrm{Where},$

$\begin{array}{rl}\therefore {B}_{2}& =\frac{{B}_{1}\mathrm{sin}{\theta }_{1}}{\mathrm{sin}{\theta }_{2}}\\ & =\frac{1.2×{10}^{-2}×\mathrm{sin}{15}^{\circ }}{\mathrm{sin}{45}^{\circ }}=4.39×{10}^{-3}\mathrm{T}\end{array}$
Hence, the maanituda if tha otharmaanatic fiale is $4.39×{10}^{-3}\mathrm{T}.$