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A short bar magnet of moment 0*32JT^-1 i...

A short bar magnet of moment `0*32JT^-1` is placed in a uniform external magnetic field of `0*15T`, if the bar is free to rotate in the plane of the field, which orientations would correspond to its, (i) stable and (ii) unstable equilibrium? What is the potential energy of the magnet in each case?

Text Solution

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Here, `M=0*32JT^-1`, `B=0*15T`
(i) In stable equilibrium, the bar magnet is aligned along the magnetic fiel, i.e. `theta=0^@`
Potential Energy `=-MB cos 0^@=-0*32xx0*15xx0=-4*8xx10^-2J`
(ii) In unstable equilibrium, the magnet is so oriented that magnetic moment is at `180^@` to the magnetic field i.e. `theta=180^@`
Potential energy=`-MB cos 180^@=-0*32xx0*15(-1)=4*8xx10^-2J`.
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