Define Magnetic Dipole Moment of a Current Carrying Loop | SI unit and Dimensional formula .
When current flows in a circular loop, magnetic field is set up around the current loop. The circular current loop behaves as a magnetic dipole. One face of the loop behaves as a North pole and the other face behaves as a South pole. The polarity of the face of circular current loop is determined by Clock Rule. If current round the face of loop or coil is in anticlockwise direction, then this face of the loop behaves as a North pole. If the current round the face of the loop is clockwise, then the face of the loop behaves as a South pole.
Magnetic dipole moment ($\overrightarrow{m}$) of the current loop:
Magnetic dipole moment of a current loop is defined as the product of the current in the loop and the area of the loop. That is,
m = IA
If $r$ is the radius of the circular current loop then area of the loop, $A = \pi r^2$.
Hence, magnetic dipole moment of the circular loop having current $I$ is given b
$m = IA = \pi r^2 I \quad \dots (i)$
Magnetic dipole moment is a vector quantity ($\overrightarrow{m}$).
The direction of magnetic dipole moment is perpendicular to the plane of the circular current loop.
The direction of magnetic dipole moment of a current loop is given by the right hand thumb rule.
The curled figures shows the direction of the current in the loop and the stretched thumb gives the direction of the magnetic dipole moment ($\mathbf{m}$).
Thus, magnetic dipole moment of a current loop is written as :
$ \overrightarrow{m} = I \overrightarrow{A} = IA(\hat{n}) \quad \dots (\text{ii})$
where $\mathbf{\hat{n}}$ is the unit vector perpendicular to the plane of the current loop and directed upward if current is anticlockwise and directed downward if current is clockwise.
SI unit of magnetic dipole moment is ampere $metre^2$ (i.e., A m$^2$).
Dimensional formula of magnetic dipole moment is $[ML^{2}T^{0}A]$.