Magnetic Dipole Moment Calculator

Enter the number of turns, current, and loop area to find the magnetic dipole moment (m = N × I × A), then see the torque and potential energy it produces in an external magnetic field.

Quick Facts

Dipole moment formula
m = N × I × A
SI unit: ampere-square meter (A·m²), equivalent to joule per tesla (J/T).
Torque in a field
τ = m × B × sin θ
Maximum torque occurs when the moment is perpendicular to the field (θ = 90°).
Potential energy
U = −m × B × cos θ
Lowest (most stable) when the moment aligns with the field (θ = 0°).

Your Results

Calculated
Magnetic Dipole Moment
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m = N × I × A, in A·m²
Maximum Torque
-
τ_max = m × B, in N·m
Torque at Given Angle
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τ = m × B × sin θ
Potential Energy
-
U = −m × B × cos θ

Ready

Enter the loop's turns, current, and area, plus the field and angle, then press Calculate.

Formula and Method for Magnetic Dipole Moment

A magnetic dipole moment describes the strength and orientation of a magnetic source, such as a current-carrying loop or coil. For a planar loop of wire, the moment is the product of the number of turns, the current flowing through them, and the loop's enclosed area: m = N × I × A, measured in ampere-square meters (A·m²). This calculator also finds the torque and potential energy that moment experiences when placed in an external magnetic field.

How the calculation works

Enter the number of turns N, the current I in amps, and the loop's enclosed area A (choosing its unit). The calculator converts the area to square meters and multiplies the three values to get the magnetic dipole moment, m = N × I × A. If you also enter an external magnetic field B and the angle θ between the moment vector and the field, the tool computes the torque τ = m × B × sin θ (with its maximum value τ_max = m × B at θ = 90°) and the potential energy U = −m × B × cos θ, which is most negative — the most stable orientation — when the moment is aligned with the field at θ = 0°.

Common mistakes

  • Forgetting the number of turns: a coil with 50 turns has 50 times the dipole moment of a single loop carrying the same current through the same area — leaving N at 1 for a multi-turn coil badly understates m.
  • Mixing area units: convert the loop's area to square meters before comparing results; a 100 cm² loop is 0.01 m², not 100 m².
  • Confusing torque with maximum torque: τ = m × B × sin θ only equals the maximum value m × B when θ = 90°; at other angles the actual torque is smaller, and it is zero when the moment is parallel or antiparallel to the field.

Real-world applications

  • Electric motors and generators rely on the torque a magnetic dipole (the rotor coil) experiences in a magnetic field to convert between electrical and mechanical energy.
  • Galvanometers and analog meters use coil dipole moment and torque balance to deflect a needle proportional to current.
  • MRI and NMR spectroscopy depend on the magnetic dipole moments of atomic nuclei aligning and precessing in strong external fields.
  • Compass needles and bar magnets are modeled as magnetic dipoles that experience torque aligning them with Earth's magnetic field.

Frequently Asked Questions

What is the formula for the magnetic dipole moment of a current loop?
For a coil of N turns carrying current I and enclosing area A, the magnetic dipole moment is m = N × I × A. Its direction is given by the right-hand rule: curl your fingers in the direction of current flow and your thumb points along m.
What are the SI units of magnetic dipole moment?
Magnetic dipole moment is measured in ampere-square meters (A·m²), which is equivalent to joules per tesla (J/T) since torque (in N·m, or joules) equals moment times field strength (in tesla).
What is the maximum torque a magnetic dipole can experience?
The torque on a dipole in a field is τ = m × B × sin θ, where θ is the angle between the moment and the field. This is maximum, τ_max = m × B, when the moment is perpendicular to the field (θ = 90°), and zero when the moment is parallel or antiparallel to the field.
Why is the potential energy negative when the moment aligns with the field?
Potential energy is U = −m × B × cos θ. At θ = 0° (moment parallel to the field), cos θ = 1, so U reaches its most negative value — the lowest-energy, most stable orientation. At θ = 180° (antiparallel), U is at its most positive and least stable.

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