Question

The unit of magnetic moment is
A) $ T{J^{ - 1}} $
B) $ J{T^{ - 1}} $
C) $ A{m^{ - 2}} $
D) $ A{m^{ - 1}} $

Answer 1

Hint The magnetic moment is a determination of its tendency to get arranged through a magnetic field and is related to the torque of an object placed in a magnetic field. Use the formula of torque acting on a body when it’s placed in a magnetic field to determine the units of the magnetic moment

Formula used:
 $\Rightarrow \tau = m \times B $ where $ \tau $ is the torque acting on an object with a magnetic moment $ m $ when placed in a magnetic field of strength $ B $

Complete step by step answer
The magnetic moment is a determination of its tendency to get arranged through a magnetic field. When placed in a magnetic field, a magnet will tend to rotate such that it can align itself with the external magnetic field. The magnetic moment determines its tendency to align with the magnetic field. The torque acting on a magnet when placed in a magnetic field can be determined as
 $\Rightarrow \tau = m \times B $
In the above equation, $ \tau $ is the torque associated with the rotating magnet which is measured in the units Joules (J), and $ B $ is the strength of the external magnetic field which is measured in Teslas (T). So we can calculate the magnetic moment as
 $\Rightarrow m = \dfrac{\tau }{B} $ which has the units
$\Rightarrow m = \dfrac{{{\text{Joules}}}}{{{\text{Tesla}}}} = J/T $ or $ J{T^{ - 1}} $ which corresponds to option B.

Note
The direction of the torque is such that the magnet aligns with the external field. This is why a compass will align its poles with the Earth’s magnetic North and South Pole. An alternative definition of the magnetic moment is also the product of the current and the area of a current-carrying loop when placed in an external magnetic field. So
 $\Rightarrow m = IA $
The units of magnetic moment can then be calculated as
 $\Rightarrow [m] = A{m^2} $ which is similar to option (C) but not exactly hence option (C) is incorrect.