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A magnetic dipole is under the influence...

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?

Text Solution

Verified by Experts

Here, `theta=60^@`, `B_1=1.2xx10^-2tesla`,
`theta_1=15^@`, `theta_2=60^@-15^@=45^@`.
In equilibrium, torque due to two fields must balance i.e.
`tau_1=tau_2`
`MB_1sintheta_1=MB_2sintheta_2`
`B_2=(B_1sintheta_1)/(sintheta_2)=(1.2xx10^-2sin15^@)/(sin45^@)`
`B_2=(1.2xx10^-2xx0.2588)/(0.7071)=4.4xx10^-3tesla`
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