Magnetic Dipole Moment Calculator

The magnetic dipole moment (μ) is a vector quantity that measures the strength and direction of the magnetic field produced by a current loop or magnet. It tells you how strongly the loop will respond to an external magnetic field and how strong a field it generates. The SI unit is ampere-square metre (A·m²).

For a single current-carrying loop, the magnetic dipole moment is μ = I × A, where I is the current in amperes and A is the area of the loop in square metres. The direction of μ is perpendicular to the plane of the loop, following the right-hand rule.

For a solenoid with N turns, the formula becomes μ = N × I × A. Each turn of wire contributes equally, so the total magnetic moment is simply the single-loop moment multiplied by the number of turns. A 100-turn solenoid with 2 A and a 0.01 m² cross-section has μ = 100 × 2 × 0.01 = 2 A·m².

The SI unit of magnetic dipole moment is the ampere-square metre (A·m²). It can also be expressed as joules per tesla (J/T), since a magnetic dipole in a field of 1 T with moment 1 A·m² stores 1 J of potential energy.

A magnetic dipole placed in a non-uniform field experiences a force proportional to the gradient of the field: F = ∇(μ · B). In a uniform field, the dipole experiences only a torque (τ = μ × B) that aligns it with the field, but no net translational force. Non-uniformity is required to produce a net force.

In practice, the two terms are used interchangeably for most applications. Technically, the magnetic moment refers to the general magnetization of an object, while the magnetic dipole moment specifically describes the dipole term in the multipole expansion of the magnetic potential. For current loops and small magnets, both refer to the same quantity μ = I·A.

The dipole model is a very good approximation when you are far enough from the magnet — typically at a distance greater than about 3 times the magnet's largest dimension. Closer than that, higher-order multipole terms become significant and the simple dipole formula underestimates field complexity. For engineering purposes, a rule of thumb is to apply the dipole model only beyond 3–5 magnet diameters.

Since the area of a circular loop is A = π × r², the magnetic moment scales with the square of the radius: μ = I × π × r². Doubling the radius quadruples the magnetic moment (assuming current is constant). This is why larger coils are significantly stronger magnetic dipoles even with the same current.