Question

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of ${75}^o$. One of the fields has a magnitude of $15mT$. The dipole attains stable equilibrium at an angle of ${30}^o$ with this field. The magnitude of the other field (in $mT$) is close to:

• A. $1$
• B. $36$
• C. $11$
• D. $1060$

Answer 1

Answer: (C)

$11$

Torque on a dipole is given by: $\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}$

where: $M:$ Magnetic moment, $B:$ Magnetic flux density

It is given that the dipole is in equilibrium. Hence, the configuration of the magnetic field vectors and the magnetic moment is as shown in the figure so that the torque due to the two fields are opposite in direction.

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

${MB}_1\sin \left({30}^o\right)={MB}_{2}sin\left({45}^o\right)$

$B_2=\frac{15\times \frac{1}{2}}{\frac{1}{\sqrt{2}}}$

$B_2=10.6mT\approx 11mT$