Magnetic Force Between Current-Carrying Wires Calculator

Parallel wires attract when their currents flow the same way and repel when opposite.

How the Math Works

The formula F/L = μ₀·I₁·I₂ ÷ (2π·d) calculates the magnetic force per unit length between two parallel current-carrying wires. Here, μ₀ (permeability of free space) is a constant (~4π×10⁻⁷ T·m/A), I₁ and I₂ are the currents in the wires, and d is their separation distance. The force increases with stronger currents and decreases with greater distance. The direction depends on current flow: parallel currents attract, while opposite currents repel. This relationship arises from the magnetic fields generated by each wire interacting with the other's current.

Practical Applications

This calculator is essential for engineers designing electrical systems like power transmission lines, where magnetic forces between parallel conductors must be managed to prevent structural damage or unsafe sagging. It also applies to crafting precision devices such as electromagnets, motors, and transformers, where controlled magnetic interactions are critical. By quantifying forces, engineers optimize wire spacing, current ratings, and material choices to ensure safety, efficiency, and reliability in real-world systems.

Day-to-Day Use

While most people don’t calculate these forces directly, the principles underpin everyday technologies. For instance, power lines strung across neighborhoods rely on this math to maintain stability despite thermal expansion and electromagnetic interactions. Similarly, the compact design of speakers, headphones, and electric vehicle motors depends on understanding how current-carrying coils interact magnetically. Without this knowledge, the safe and efficient operation of modern electronics, appliances, and energy infrastructure would be impossible.

Worked example

10 A and 10 A, 10 mm apart, 1 m → about 2 × 10⁻³ N.

FAQ