A magnetic dipole is under the influence of two magnetic fields. The angle between the two field directions is `60^(@)` and one of the fields has a magnitude of `1.2xx10^(-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

Given, the angle between two fields = `60^@`
The magnitude of the first field, `B_1 = 1.2 xx 10^(-2) T`
Let `B_2 ` be the magnitude of the other field. In equilibrium, torque exerted by each field on the dipole are equal.
` tau_1 = tau_2`
`MB_1 sin 15^@ = MB_2 sin 45^@`
`B_2 = (B_1 sin 45^@)/(sin 45^@)`
` = (1.2 xx 10^(-2) sin 15^@)/(sin 45^@) = 4.4 xx 10^(-3) T`