Question

A magnetic dipole is under the influence of two orthogonal magnetic fields, $B_{1}=0.5 \times 10^{-3} T$ and $B_{2}=0.866 \times 10^{-3} T .$ If the dipole comes to stable equilibrium at an angle $\theta$ with respect to $B_{2}$ field, then the value of $\theta$ is

• A. $45^{\circ}$
• B. $30^{\circ}$
• C. $60^{\circ}$
• D. $90^{\circ}$

Answer 1

Answer: (B)

From tangent law, we have,
$m B_{2} \sin \theta=m B_{1} \sin \left(90^{\circ}-\theta\right)$

$\Rightarrow \tan \theta =\frac{B_{1}}{B_{2}}=\frac{0.5 \times 10^{-3}}{0.866 \times 10^{-3}} $
$=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}$
$\tan \theta=\tan 30^{\circ}$
$\Rightarrow \theta=30^{\circ}$