Question

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60°, and one of the fields has a magnitude of 1.2 × 10–2 T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field?

Answer 1

A magnetic dipole is under the influence of two magnetic fields. The angle between the field and direction 60, and one of the fields has a magnitude, $B_1=1.2\times10^{-2}T$.

a/c to question, dipole comes to stable equilibrium at an angle 15° with above field.

The magnetic dipole experience torque due to both the fields $B_1,B_2$ and is in stable equilibrium.

$MB_1sin\theta_1=MB_2sin\theta_2$

or, $B_1sin\theta_1=B_2sin\theta_2$

see diagram,

angle between dipole and $B_1$, $\theta_1=15^{\circ}$

and angle between dipole and $B_2$, $\theta_2=45^{\circ}$

or, 1.2 × 10^-2 × sin15° = $B_2$sin45°

or, $B_2$ = 0.44 × 10^-2 T.