The magnetic moment (μ) is a property of a magnet or a current-carrying object that measures its tendency to align with an external magnetic field. Think of it as a vector that points from the south pole to the north pole of a magnet. The stronger the magnet, the larger its magnetic moment. For a current-carrying coil of wire, the magnetic moment indicates the strength and direction of the magnetic field it creates.
For a flat loop of wire with a current, the magnetic moment is a vector defined by the following equation:
M=NIAB
Where:
M is the magnetic moment vector, measured in Ampere-meters squared (A·m²).
N is the number of turns in the coil.
I is the current flowing through the wire, measured in Amperes (A).
A is the area vector of the loop. Its magnitude is the area of the loop, and its direction is perpendicular to the plane of the loop.
B is the strenght of magnetic field.
You can determine the direction of the magnetic moment using the Right-Hand Rule:
Curl the fingers of your right hand in the direction of the current flowing around the loop.
Your thumb will point in the direction of the magnetic moment (μ). This direction also corresponds to the North pole of the magnetic field created by the loop.