A current loop behaves like a tiny bar magnet. Its magnetic moment determines how strongly it aligns with a field – the principle of electric motors, galvanometers and MRI.
How to use the Magnetic Dipole Moment Calculator
- Current I
- Loop given by
- Loop radius r
- Loop area A
- Number of turns N
- External field B (optional)
- Angle θ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the current, the loop radius or area, the number of turns and optionally a magnetic field and angle for the torque.
Inputs explained
| Field | What to enter |
|---|---|
| Current I | Units: A, mA, µA, kA |
| Loop given by | Choose one: Radius, Area |
| Loop radius r | Units: cm, mm, m, in, ft |
| Loop area A | Units: cm², m², mm² |
| Number of turns N | A number |
| External field B (optional) | Units: T, mT, µT, G, nT |
| Angle θ | Units: °, rad, arcmin, arcsec, mrad |
What each result means
- Magnetic dipole moment μ = [Number of turns N]×[Current I]×[A]
- Torque in the field = [Number of turns N]×[Current I]×[A]×[External field B (optional)]×sin(rad([Angle θ]))
Example values
How the main result changes when Current I changes and everything else stays at the example values above:
| Current I (A) | Magnetic dipole moment μ (A·m²) |
|---|---|
| 1 | 0.2827 |
| 1.5 | 0.4241 |
| 2 | 0.5655 |
| 2.5 | 0.7069 |
| 3 | 0.8482 |
| 4 | 1.131 |
Formula
μ = N·I·A, τ = μ·B·sin θ
Worked example
Inputs — Current I: 2 A; Loop given by: Radius; Loop radius r: 3 cm; Number of turns N: 100; External field B (optional): 0.1 T; Angle θ: 90 °.
Results — Magnetic dipole moment μ = 0.565487 A·m²; Torque in the field = 0.05655 N·m.
Key terms
- Magnetic moment
- Strength and orientation of a magnetic dipole.
Frequently asked questions
What is the unit of magnetic moment?
A·m² (equivalently J/T).
Why does a loop act like a magnet?
The circulating current produces a dipole field.
When is the torque maximum?
When the moment is perpendicular to the field.
What is the Bohr magneton?
The natural unit of electron magnetic moment, 9.274 × 10⁻²⁴ J/T.