(a) Consider a planar square loop with current I and side l. The loop is positioned in a uniform magnetic field \(\vec{B}\). There is an angle \(\theta\) between the normal to the loop and \(\vec{B}\). Find the torque \(\vec{\tau}\) on the loop. Show that your answer agrees with the general relation (that we will not prove)
\(\vec{\tau} = \vec{m} \times \vec{B}\).
(b) Consider a magnetic moment \(\vec{m}\) positioned in a magnetic field \(\vec{B}\). Consider the work done by the magnetic field in torquing the dipole to align with the field. Show that if the zero of potential energy is taken to be when \(\vec{m} \perp \vec{B}\), then the potential energy of the dipole is
\(U(\theta) = -\vec{m} \cdot \vec{B}\)
(c) Complete the following sentences, and erase the incorrect parts
1. Paramagnetism is due to the alignment / anti-alignment of (......) with (....). If you put a paramagnetic material near a magnet it will attract / repel.
2. Diamagnetism is due to the alignment / anti-alignment of (......) with (....). If you put a paramagnetic material near a magnet it will attract / repel.
Note that the (...) may involve few words (not just one), but shouldn't involve many sentences.
