First slide

Magnetic dipole in a uniform magnetic field

Question

A short bar magnet placed with its axis at 30^o with a uniform external magnetic field of 0.16 T experiences a torque of magnitude 0.032 Nm. If the bar magnet were free to rotate, its P.E when it is in stable and unstable equilibrium are respectively.

Moderate

A

–0.064 J, +0.064 J
B

–0.032 J, +0.032 J
C

+0.064 J, –0.064 J
D

+0.032 J, -0.032 J

Solution

$\begin{array}{rcl} τ & = & MB \sin 30 = 0.032; \\ MB & = & 0.064 \\ PE (U) & = & - MBcosθ \end{array}$
Stable $θ$ = 0^o , U = -0.064 J
Unstable $θ$ = 180^o, U = +0.064 J

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