The magnetic potential energy $ U $ of a magnetic dipole moment $ \vec{m} $ in a magnetic field $ \vec{B} $ is given by the formula:

$$ U = -\vec{m} \cdot \vec{B} $$

Here, the dot product $ \vec{m} \cdot \vec{B} $ represents the scalar product of the vectors. When the magnetic moment $ \vec{m} $ is placed perpendicular to the magnetic field $ \vec{B} $, the angle $ \theta $ between these two vectors is 90 degrees. The dot product in this case can be written as:

$$ \vec{m} \cdot \vec{B} = m B \cos \theta $$

Since $ \theta = 90^\circ $, we have $ \cos 90^\circ = 0 $. Therefore, the magnetic potential energy $ U $ becomes:

$$ U = -m B \cos 90^\circ $$

$ U = -m B \cdot 0 $

$ U = 0 $

So, the magnetic potential energy when a magnetic bar of magnetic moment $ \vec{m} $ is placed perpendicular to the magnetic field $ \vec{B} $ is zero.

The correct answer is: Option B "Zero".