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*2xx10^-2` tesla. If the dipole comes to stable equilibrium at an angle of `15^@` with this field, figure, what is the magnitude of the other field?

Explanation

Magnitude of one of the magnetic fields, `B_(1)=1.2xx10^(-2)T`
Magnitude of the other magnetic field`=B_(2`
Angle betweenthe two fields , `theta=60^(@)`.
At stable equilibrium the angel between the dipole and field `B_(1),tehta_(1)=15^(@)`
Angle between the dipole and field `B_(2),theta_(2)-theta_(1)=60^(@)-15^(@)=45^(@)`
At rotational equilibrium the torques between both the fields must balance each other.
`therefore `Torque due to field `B_(1)=` Torque due to field `B_(2)`
`MB_(1)sintehta_(1)=MB_(2)sin theta_(2)`
where,
M=Magnetic moment of the dipole
`thereforeB_(2)=(B_(1)sin theta_(1))/(sin theta_(2))`
`=(1.2xx10^(-2)xxsin15^(@))/(sin45^(@))=4.39xx10^(-3)T`
Hence, the magnitude of the other magnetic field is 4.39`xx10^(-3)T`.