A magnetic dipole is under the influence of two magnetic fields. The angle between the field direction is 60° and one of the fields has a magnitude of `1.2 xx 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?

Explanation

Here `B_1 = 1.2 xx 10^(-2)T`
Inclination of dipole with `B_1 ` is ` theta_1 = 15^(@)`
Therefore , inclination of dipole with `B_2` is
` theta_2 = 60^@ - 15^(@) = 45^(@)`

As the dipole is in equilibrium , therefore the torque on the dipole due to the two fields are equal and opposite . If M is magnetic dipole moment of the dipole , then
`MB_1 sin theta_1 =MB_2 sin theta_2 or B_2 = ( B_1 sin theta_1)/(sin theta_2)`
`=(1.2 xx 10^(-2) xx 0.2588)/(0.707) = 4.39 xx 10^(-3)T`