A bar magnet with a magnetic moment 5.0 A m$$^2$$ is placed in parallel position relative to a magnetic field of 0.4 T. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is ________.

The work done in rotating a magnetic dipole in a uniform magnetic field is:

$$ W = -mB(\cos\theta_2 - \cos\theta_1) $$

where $$m = 5.0$$ A m$$^2$$, $$B = 0.4$$ T.

Initial position: parallel ($$\theta_1 = 0°$$)

Final position: antiparallel ($$\theta_2 = 180°$$)

$$ W = -mB(\cos 180° - \cos 0°) = -5.0 \times 0.4 \times (-1 - 1) $$

$$ W = -2.0 \times (-2) = 4 \text{ J} $$

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