A magnetic dipole is acted upon by two magnetic fields which are inchined to each other at an angle of $75°.$ One of the fields has a magnitude of $15 mT$. The dipole attains stable equilibrium at an angle of $30°$ with this field. The field (in $mT$) is close to

The magnetic dipole attains stable equilibrium under the influence of these two fields making an angle ${\theta }_1=30°$ with $B_1$ and ${\theta }_2=75°-30°=45°$ with $B_2.$

For stable equilibrium, net torque acting on dipole must be zero, i.e., ${\overrightarrow{\tau }}_1+{\overrightarrow{\tau }}_2=0$ or ${\tau }_1={\tau }_2$

or $m{B}_1\sin {\theta }_1=m{B}_2\sin {\theta }_2$

$$\begin{gathered} \Rightarrow B_2=B_1\frac{\sin {\theta }_1}{\sin {\theta }_2} \\ =15\mathrm{mT}\times \frac{\sin 30°}{\sin 45°} \\ =15\mathrm{mT}\times \frac{1}{2}\times \sqrt{2}=10.6{\mathrm{mT}}^{\text{'}}\approx 11\mathrm{mT} \end{gathered}$$