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 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

As shown in Fig. Let `vecB_1 =1.2xx10^(-2) T ` and `vecB_2` be inclined at an angle `60^@` from `vecB_1`
The magnetic dipole n s comes to stable equilibrium at an angle of `15^@` with the field `vecB_1`. It means that net torque acting on the magnetic dipole must be zero i.e., `vectau_1 + vectau_2 = 0 ` or `|vectau_1 | = |vectau_2|`

`implies mB_1 sin 15^@ = mB_2 sin (60^@ - 15^@)`
`implies B_1 sin 15^@ = B_2 sin 45^@`
`therefore B_2 = (B_1 sin 15^@)/(sin 45^@) =((1.2 xx 10^(-2))xx0.2588)/(0.7071) =4.39 xx 10^(-3) T ~=4.4 xx 10^(-3) T`