A short bar magnet placed with its axis at `30^@` experiences a torque of `0*016N-m` in an external field of `800G`.
(a) What is the magnetic moment of the magnet? (b) What is the work done by an external force in moving it from its most stable to most unstable position? (c) What is the work done by force due to external magnetic field in the process mentioned in (b)? (d) The bar magnet is replaced by solenoid of cross sectional area `2xx10^-4m^2` and `1000` turns, but the same magnetic moment. Determine the current flowing through the solenoid.

Explanation

(a) Here, `theta=30^@`, `B=800xx10^-4T`,
`tau=0*016Nm, M=?`
As `tau=MB sin theta`
`:. M=(tau)/(Bsintheta)=(0*016)/(800xx10^-4xxsin30^@)`
(b) For most stable position, `theta=0^@` and for most unstable position, `theta=180^@`
`:.` work done by external force
`=-MB(cos180^@-cos0^@)=2MB`
`=2xx0*40xx800xx10^-4`
`=0*064J`
(c) Work done by external mag. field
`=-0*064J`
(d) As `M=NIA`
`:. 0*40=1000xxIxx2xx10^-4`,
`I=(0*40)/(0*2)=2A`