Magnetic Moment Calculator

A current loop creates a magnetic dipole — it behaves like a tiny bar magnet. The magnetic moment vector is:

$$\vec{m} = nI\vec{A}$$

where $$\vec{A}$$ is the area vector (perpendicular to the loop, direction given by the right-hand rule with current). For a coil with n turns, each turn contributes equally, multiplying the moment by n.

When placed in an external magnetic field B, the dipole experiences:

• Torque: $$\tau = mB\sin\theta$$, where θ is the angle between m and B. This torque tends to align the moment with the field.
• Potential energy: $$U = -mB\cos\theta$$. Energy is minimized (most stable) when m is aligned with B (θ = 0°), and maximized when anti-aligned (θ = 180°).

The magnetic moment has units of A·m² (ampere-square meters), equivalent to J/T (joules per tesla). For atoms, the Bohr magneton $$\mu_B = 9.274 \times 10^{-24}\,\text{A·m²}$$ is the natural unit of magnetic moment.

Applications span from macroscopic motors (where coil moment × field = torque) to quantum mechanics (where electron spin and orbital magnetic moments determine atomic spectra and magnetic resonance phenomena).

The magnetic moment tells you the strength of the equivalent magnetic dipole. Larger moments mean stronger interaction with external fields. The torque indicates how strongly the field tries to rotate the coil — maximum at θ = 90° and zero when aligned. The potential energy shows the energetic cost of misalignment with the field. For motor design, maximizing m (more turns, higher current, larger area) increases torque output.