What Is the Magnetic Dipole Moment?
The magnetic dipole moment m measures the strength and orientation of a magnetic source, such as a current-carrying loop or coil. For a flat coil it equals the product of the number of turns, the current flowing through it, and the area enclosed by each loop. The SI unit is the ampere square metre (A·m²). This tool is universal — it applies to any physics or engineering problem, with no regional restrictions.
How to Use This Calculator
Enter three values: the number of turns N in the coil, the current I in amperes flowing through the wire, and the area A of a single loop in square metres. The calculator multiplies them together to return the magnetic dipole moment instantly. For a circular loop of radius r, the area is \(A = \pi r^2\); for a rectangular loop it is length \(\times\) width.
The Formula Explained
The governing equation is $$m = \text{N} \cdot \text{I} \cdot \text{A}$$ Each turn of wire contributes its own current loop, so N turns multiply the effect. The moment is a vector pointing along the coil's axis, given by the right-hand rule, but this calculator returns its magnitude. The moment determines the torque \(\tau = m \times B\) that a coil experiences in an external magnetic field B.
Worked Example
Consider a coil with \(N = 100\) turns, carrying \(I = 2\) A, with each loop enclosing \(A = 0.01\) m². Then $$m = 100 \times 2 \times 0.01 = 2 \ \text{A}\cdot\text{m}^2$$ If this coil sat in a 0.5 T field perpendicular to its moment, it would feel a torque of \(2 \times 0.5 = 1 \ \text{N}\cdot\text{m}\).
FAQ
What units does the result use? Ampere square metres (A·m²), the SI unit of magnetic dipole moment.
Does loop shape matter? Only through the enclosed area A — a circle, square or any shape with the same area gives the same moment.
What if I have a single loop? Set \(N = 1\) and the formula reduces to \(m = \text{I} \cdot \text{A}\).
