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

Here `theta = 60^(@), B_(1) = 1.2 xx 10^(-2)` tesla
`theta_(1) = 15^(@), theta_(2) = 60^(@) - 15^(@) = 45^(@)`
In equilibrium, torque due to two fields must balance i.e., `r_(1) = r_(2)`
`MB_(1) sin theta_(1) = MB_(2) sin theta_(2)`
`B_(2) = (B_(1) sin theta_(1))/(sin theta_(2)) = (1.2 xx 10^(-2) sin 15^(@))/(sin 45^(@))`
`B_(2) = (1.2 xx 10^(-2) xx 0.2588)/(0.7071) = 4.4 xx 10^(-3)` tesla.