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A compass needle whose magnetic moment i...

A compass needle whose magnetic moment is `60Am^2` pointing geographic north at a certain place where horizontal component of earth's magnetic field is `40muWb//m^2` experiences a torque of `1*2xx10^-3Nm`. What is the declination of the place?

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Here, `M=60Am^2`,
`H=40mu Wb//m^2=40xx10^-6 Wb//m^2`
`tau=1*2xx10^-3Nm`. Declination, `theta=?`
As is known, in stable equilibrium, a compass needle points along magnetic N-S and experiences no torque. But when compass needle is turned through angle of declination `(theta)`, it points towards geographic N-S and experience torque,
`tau=MB sin theta`
`sin theta=(tau)/(MB)=(1*2xx10^-3)/(60xx40xx10^-6)=1/2`
`theta=30^@`
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