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)

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. ${\tau }_1={\tau }_2$
$\Rightarrow M{B}_{1}sin{\theta }_1=M{B}_{2}sin{\theta }_2$
or $B_2=B_1\frac{sin{\theta }_1}{sin{\theta }_2}$
$=B_2=\frac{sin30^{\circ }}{sin30^{\circ }}=B_1$
$=1.2\times 10^{-2}T$