Magnetic Dipole Moment Calculator

Calculate the magnetic dipole moment of a current loop or bar magnet based on current, area, and number of turns.

MAGNETIC DIPOLE MOMENT
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Moment (A·m²)
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Current
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Total Area
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Turns
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What Is a Magnetic Dipole Moment?

The magnetic dipole moment is a vector quantity that measures the strength and orientation of a magnetic source. For a current loop, it equals the product of the current, the loop area, and the number of turns. The magnetic dipole moment determines how strongly a magnet or current loop interacts with an external magnetic field, experiencing torque that tends to align it with the field.

Magnetic dipole moments appear at all scales of physics: from elementary particles (electron spin magnetic moment), through atoms (orbital and spin contributions), to macroscopic objects (solenoids, permanent magnets, MRI coils). The concept is central to understanding magnetism in materials, NMR spectroscopy, and electromagnetic devices.

The Formula

m = N I A
τ = m × B = mB sin(θ)

Where m is the magnetic moment (A·m²), N is number of turns, I is current (A), A is loop area (m²), and τ is the torque experienced in field B.

Applications

ApplicationTypical MomentNotes
Electron spin9.274 × 10-24 A·m²Bohr magneton
MRI coil0.1-10 A·m²Gradient and RF coils
Compass needle0.05-1 A·m²Permanent magnet
Earth7.94 × 1022 A·m²Geomagnetic field

Frequently Asked Questions

How does a magnetic moment relate to torque?

When a magnetic dipole is placed in an external magnetic field B, it experiences a torque τ = m x B that tends to align the moment with the field. The magnitude is τ = mB sin(θ), where θ is the angle between the moment and the field. This is the principle behind electric motors, galvanometers, and compass needles.

What is the Bohr magneton?

The Bohr magneton (μB = 9.274 x 10-24 J/T) is the natural unit of magnetic moment for electrons. It equals eℏ/(2me), where e is the electron charge, ℏ is the reduced Planck constant, and me is the electron mass. Atomic magnetic moments are typically expressed as multiples of the Bohr magneton.

What is the difference between magnetic moment and magnetization?

Magnetic moment (m) is a property of an individual loop, atom, or magnet. Magnetization (M) is the magnetic moment per unit volume of a material: M = m/V. Magnetization characterizes the bulk magnetic behavior of a material and is related to the magnetic field inside the material by B = μ0(H + M).