Question

A permanent magnet has a magnetic dipole moment of 0.120 A · m². The magnet is in the presence of an external uniform magnetic field (provided by current-carrying coils) with a magnitude of 0.0800 T, which makes an angle of 18.0° with the orientation of the permanent magnet.

(a)

What is the magnitude of the torque (in N · m) on the permanent magnet?

-------------- N . m

(b)

What is the potential energy (in J) of the system consisting of the permanent magnet and the magnetic field provided by the coils?

-------------------- J

Answer 1

Torque is given by

$\vec{N}=\vec{m}\times\vec{B}$

so the magnitude is

$N=mB\sin\theta$

$N=2.96\times10^{-3}\textup{ N-m}$

P.E. associated with the system is

$U=-\vec{m}\cdot\vec{B}=-mB\cos\theta$

$U=-9.13\times10^{-3}\textup{ J}$