Magnetic Force Between Wires Calculator

When current flows through a wire, it generates a magnetic field around it (as described by Ampere's law). A neighboring wire carrying its own current sits inside that magnetic field, and by the Lorentz force law, a current-carrying conductor in a magnetic field experiences a force. The result is a mutual force between the two wires that depends on both currents and their separation.

The force per unit length is given by F/L = μ₀ × I₁ × I₂ / (2π × d), where μ₀ = 4π × 10⁻⁷ T·m/A is the permeability of free space, I₁ and I₂ are the currents in each wire (in Amperes), and d is the center-to-center separation between the wires (in meters). Multiply F/L by the wire length L to get the total force in Newtons.

Wires carrying current in the same direction attract each other, while wires carrying current in opposite directions repel each other. This can be understood using the right-hand rule: the magnetic field created by one wire exerts a force on the other wire in a direction that depends on the relative orientation of the currents.

μ₀ = 4π × 10⁻⁷ T·m/A is a physical constant that describes how easily a magnetic field forms in a vacuum. It appears in the force formula because the interaction between the wires is mediated by the magnetic field, whose strength in free space is governed by μ₀. In materials with higher magnetic permeability, the force would be proportionally stronger.

The magnetic force between wires is inversely proportional to the distance d between them. Halving the separation doubles the force per unit length, while doubling the separation halves the force. This means wires that are very close together can experience significantly large forces, which is an important design consideration in high-current applications like busbars and transformer windings.

Engineers use this calculation in the design of power transmission busbars, electric motor windings, transformer coil spacing, and substation structures. During short-circuit faults, currents can reach thousands of Amperes, producing forces that can mechanically damage equipment if the structural design does not account for them. Proper spacing and bracing of conductors is guided directly by this formula.

The fundamental result from electromagnetic theory is the force per unit length (F/L), which is independent of wire length. To find the total force on a finite segment, you multiply F/L by the length L of the wire. For infinitely long parallel wires, only the force per unit length is physically meaningful.

Historically, the Ampere was defined as the constant current that, when flowing in two straight parallel conductors of infinite length placed 1 meter apart in vacuum, produces a force of 2 × 10⁻⁷ N per meter of length between them. This definition was replaced in 2019 by a definition based on fixing the elementary charge, but the relationship remains a fundamental result of electromagnetism.