Question

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is $60^{\circ}$ and one of the fields has a magnitude of $1.2 \times 10^{-2}\, T$. If the dipole comes to stable equilibrium at an angle of $30^{\circ}$ with this field, then the magnitude of the field is

• A. $1.2 \times 10^{-4}\,T$
• B. $2.4 \times 10^{-4}\,T$
• C. $1.2 \times 10^{-2}\,T$
• D. $2.4 \times 10^{-2}\,T$

Answer 1

Answer: (C)

$1.2 \times 10^{-2}\,T$

Answer 2

Here, $\theta = 60^{\circ}$, $B_{1} = 1.2 \times 10^{-2}\,T$ $\theta_{1} = 30$ and $\theta_{2} = 60^{\circ } - 30^{\circ} = 30^{\circ}$ in stable equilibrium, torques due to two fields must be balanced i.e. $\tau_{1} = \tau_{2}$ $\Rightarrow\quad MB_{1}\, sin\, \theta_{1} = MB_{2}\, sin \,\theta_{2}$ or $\quad B_{2} = B_{1} \frac{ sin \,\theta _{1}}{ sin \,\theta _{2}}$ $= B_{2} = \frac{ sin \,30^{\circ}}{ sin \,30^{\circ}} = B_{1}$ $= 1.2 \times 10^{-2}\,T$