Question

A magnetic dipole is under the influence of two magnetic fields. The angle between the field direction is `60^(@)` and one of the fields has magnitude of `1.2 xx 10^(-2)T`. If the dipole comes to stable equilibrium at an angle of `30^(@)` with this Held, then the magnitude of the field is
A. `1.2xx10^(-4)T`
B. `2.4xx10^(-4)T`
C. `1.2xx10^(-2)T`
D. `2.4xx10^(-2)T`

Answer 1

Correct Answer - C
`"Here", theta=60^(@), B_(1)=1.2xx10^(-2)T`
`theta_(1)=30^(@) and theta_(2)=60^(@)-30^(@)=30^(@)`
in stable equilibrium, torques due to two fields myst be balanced, i.e. `tau_(1)=tau_(2)`
`Rightarrow MB_(1)sin theta_(1)=MB_(2) sin theta_(2)`
`or B_(2)-B_(1) (sin theta_(1))/(sin theta_(2))`
`or B_(2)(sin 30^(@))/(sin 30^(@))=B_(1)`
`=1.2xx10^(-2)T`