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 ${15}^o$ with this field, what is the magnitude of the other field?

• A. $3\left(\sqrt{3}-1\right)\times {10}^{-3}\text{T}$
• B. $\left(\sqrt{3}-1\right)\times {10}^{-3}\text{T}$
• C. $6\left(\sqrt{3}-1\right)\times {10}^{-3}\text{T}$
• D. $2\left(\sqrt{3}-1\right)\times {10}^{-3}\text{T}$

Answer 1

The correct option is A $3\left(\sqrt{3}-1\right)\times {10}^{-3}\text{T}$

Here, $\theta ={60}^0,B1=1.2\times {10}^{-2}tesla,$

${\theta }_1={15}^0,{\theta }_2={60}^0-{15}^0={45}^0.$

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

${\tau }_1={\tau }_2$

$M{B}_{1}sin{\theta }_1=MB2sin{\theta }_2$

$⟹1.2\times {10}^{-2}\times sin{15}^{\circ }=B_{2}sin(60-15{)}^{\circ }=B_{2}sin{45}^{\circ }$

$⟹B_2=4.4\times {10}^{-3}T$