Magnetic Force Between Current-Carrying Wires Calculator

When electric current flows through a conductor, it generates a circular magnetic field around it. If a second current-carrying wire is placed within this magnetic field, it experiences a magnetic force. The magnitude of this force per unit length (F/L) is governed by Ampère's force law. The standard formula used in this calculator is:

F / L = (μ₀ * I₁ * I₂) / (2 * π * r)

Where F/L is the magnetic force per unit length in Newtons per meter (N/m), μ₀ is the permeability of free space (approximately 4π × 10⁻⁷ T·m/A), I₁ and I₂ are the electric currents in amperes, and r is the shortest distance between the two wires in meters. When the currents flow in the same direction, the wires attract each other; when they flow in opposite directions, they repel.

Imagine two long, parallel power transmission lines separated by a small distance in air. Let us calculate the magnetic force per unit length under the following realistic parameters:

Current in Wire A (I₁): 15 Amperes

Current in Wire B (I₂): 25 Amperes

Distance between wires (r): 0.05 meters (5 cm)

Step 1: Substitute the values into the formula using the magnetic constant (2 × 10⁻⁷ N/A² for the numerator term combining μ₀ and 2π).

F / L = (2 × 10⁻⁷ × 15 × 25) / 0.05

Step 2: Multiply the currents and the constant.

F / L = (2 × 10⁻⁷ × 375) / 0.05

F / L = (7.5 × 10⁻⁵) / 0.05

Step 3: Divide by the separation distance.

F / L = 1.5 × 10⁻³ N/m or 0.0015 Newtons per meter of wire length.

Always convert your distance measurements into standard SI units (meters) before performing calculations to avoid magnitude errors. Keep in mind that currents flowing in identical directions create an attractive force, while opposing currents create repulsion, which is crucial mechanical data when mounting high-current busbars or overhead cables.