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 \( \mathbf{M} \) of a current-carrying coil is given by: \[ \mathbf{M} = I A \hat{n} \] Where: - \( I \) is the current in the coil, - \( A \) is the area of the coil, - \( \hat{n} \) is the unit vector perpendicular to the plane of the coil, indicating the direction of the dipole moment. The direction of \( \mathbf{M} \) is given by the right-hand rule. If the fingers of the right hand curl in the direction of the current, the thumb points in the direction of the magnetic dipole moment.