The physics
A current is the charge that passes a point each second. Charge going round a circle is a current loop.
I = Q f = Qω / 2π one charge on an orbit: I = qv / 2πr
A current loop makes a field at its centre, B = μ0I/2r. It also has a magnetic moment, μ = current × area.
ring: μ = QωR²/2 disc: μ = QωR²/4 charge on a ball's skin: μ = QωR²/3
For a spread-out body, cut it into thin rings and add them. An electron's current runs against its motion. So its moment points opposite to its angular momentum.
μ = −(e / 2m) L μ0 = 4π × 10⁻⁷ T m/A