Question

Obtain the relation for magnetic dipole moment \( \mathbf{M} \) of a current-carrying coil. Give the direction of \( \mathbf{M} \).

Hint:

The magnetic dipole moment of a coil is directed along the axis of the coil, and its magnitude is \( M = I A \).

Answer 1

The magnetic dipole moment, denoted by \( \mathbf{M} \), for a coil carrying current is defined as:\[ \mathbf{M} = I A \hat{n} \]Here, \( I \) represents the current flowing through the coil, \( A \) signifies the coil's area, and \( \hat{n} \) is the unit vector normal to the coil's plane, establishing the dipole moment's direction. This direction aligns with the right-hand rule: when the fingers of the right hand are curled in the direction of the current, the thumb indicates the direction of \( \mathbf{M} \).