A magnetic dipole is under the influence of trwo magnetic fields. The angle between the two field directionss is `60^(@)` and one of the fields has a magnitudeo `f1.2xx10^(-2)T`. Of the dipole comes to stable equilibrium at an angle of `15^(0)` with this field, what is the magnitude of the other field?

Explanation

Here `B_(1)=1.2xx10^(-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 mgnetic dipole moment of the dipole, then

`MB_(1) sin theta_(1)=MB_(2) sintheta_(2)` or `B_(2)=(B_(1) sin theta_(1))/(sin theta_(2))=(1.2xx10^(-2)xxsin15^(@))/(sin 45^(@)),`
`=(1.2xx10^(-2)xx0.2588)/(0.707),=4.39xx10^(-3)T`