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

• A. $4.4\times 10^{-3}$ tesla
• B. $5.2\times 10^{-3}$ tesla
• C. $3.4\times 10^{-3}$ tesla
• D. $7.8\times 10^{-3}$ tesla

Answer 1

Answer: (A)

Given that: $B_1=1.2\times 10^{-2}T$, orientation of dipole with the field $B_1,{\theta }_1=15^{\circ }$
Hence, orientation of dipole with $B_2$,
${\theta }_2=60^{\circ }-15^{\circ }=45^{\circ }$ (figure)
As the dipole is in equilibrium, therefore, the torque on the dipole due to the two fields must be equal and opposite.
If $M$ be the magnetic dipole moment of the dipole, then
${\tau }_1={\tau }_2$
or$M{B}_1\sin {\theta }_1=M{B}_2\sin {\theta }_2$
or, $B_2=\frac{B_1\sin {\theta }_1}{\sin {\theta }_2}=\frac{1.2\times 10^{-2}\sin 15^{\circ }}{\sin 45^{\circ }}$
$=\frac{1.2\times 10^{-2}\times 0.2588}{0.7071}=4.4\times 10^{-3}$ Tesla