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*25xx10^-2T`. If the dipole comes to stable equilibrium at an angle of `15^@` with this field, find the magnitude of other magnetic field.

Answer

`4*58xx10^-3T`

Explanation

Here, `B_1=1*25xx10^-2T`, `theta_1=15^@`
`theta_2=60^@-15^@=45^@`, `B_2=?`
In stable equilibrium, the torques on the dipole due to two magnetic fields are equal and opposite,
i.e., `tau_1=tau_2`
`MB_1sintheta_1=MB_2sintheta_2`
`B_2=(B_1sintheta_1)/(sintheta_2)=(1*25xx10^-2sin15^@)/(sin45^@)`
`B_2=1*25xx10^-2xx0*2588//0*7071`
`=4*58xx10^-3T`