Question

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is ${60}^o$ 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 ${30}^o$ 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

Here, $\theta ={60}^0,B_1=1.2\times {10}^{-2}T$

${\theta }_1={30}^0,{\theta }_2={60}^0-{30}^0={30}^0.$

In equilibrium, torque due to two fields must balance i.e.

$⟹{\tau }_1={\tau }_2$

$⟹M{B}_{1}sin{\theta }_1=M{B}_{2}sin{\theta }_2$

$⟹1.2\times {10}^{-2}\times sin{30}^o=B_{2}sin{30}^o$

$⟹B_2=1.2\times {10}^{-2}T$