Magnetic Moment Calculator — Torque and Energy in a Field
Find the magnetic moment of a current coil and compute the torque and potential energy it experiences when placed at an angle to an external magnetic field.
turns
A
m²
T
°
m = N · I · A
- 1
Turns × current
1 × 3 = 3 - 2
Magnetic moment m = N × I × A
3 × 0.005 = 0.015000m is the magnetic dipole moment of the coil in A·m².
How does this calculator work?
A coil of N turns, current I, and loop area A has magnetic moment m = N·I·A (A·m²). In external field B at angle θ it experiences torque τ = m·B·sin θ (N·m) trying to align it with the field, and potential energy U = −m·B·cos θ (J), which is lowest when m is aligned with B.
Formula
How this is calculated
A coil of N turns, each carrying current I and enclosing area A, has a magnetic moment m = N · I · A (in A·m²). The moment vector is perpendicular to the coil plane, with direction given by the right-hand rule for the current flow. This is the same quantity used in atomic physics (electron orbital and spin moments), bar-magnet models, and electromagnetic machines, though this calculator focuses on macroscopic coils.
When the coil is placed in an external magnetic field B at angle θ between the moment vector and the field direction, it experiences a restoring torque τ = m · B · sin θ that tries to align the moment with the field. Torque is maximum when θ = 90° and zero when the moment is aligned (θ = 0°) or anti-aligned (θ = 180°). The potential energy of interaction is U = −m · B · cos θ, which is minimised (most stable) when m is aligned with B and maximised when anti-aligned.
The diagram shows the external field B pointing upward and the magnetic moment m at the specified angle, illustrating how far the coil is from its equilibrium orientation. In motors and galvanometers, this torque drives the rotation of a current loop in a field.
Frequently asked questions
They are the same physical quantity — both equal N·I·A for a coil, or I·A for a single loop. "Dipole moment" emphasises the analogy with an electric dipole and is often used in the far-field context. "Magnetic moment" is the more general term used in engineering and atomic physics.
Torque τ = m·B·sin θ is greatest when θ = 90°, meaning the magnetic moment is perpendicular to the field. It is zero when the moment is aligned (θ = 0°, stable equilibrium) or anti-aligned (θ = 180°, unstable equilibrium) with the field.
In a DC motor, a coil (the armature) carrying current sits in a magnetic field. The torque τ = N·I·A·B·sin θ drives rotation. As the coil turns, a commutator reverses the current at θ = 0° so the torque always acts in the same rotational direction, producing continuous motion.
TG we-Calculate Editorial Team. (2026). Magnetic Moment Calculator — Torque and Energy in a Field [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/magnetic-moment-calculator
TG we-Calculate Editorial Team. "Magnetic Moment Calculator — Torque and Energy in a Field." TG we-Calculate. 2026. https://we-calculate.com/calculator/magnetic-moment-calculator.
TG we-Calculate Editorial Team, "Magnetic Moment Calculator — Torque and Energy in a Field," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/magnetic-moment-calculator
@misc{wecalculate_magnetic_moment_calculator, title = {Magnetic Moment Calculator — Torque and Energy in a Field}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/magnetic-moment-calculator}}, year = {2026}, note = {TG we-Calculate} }
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