# Magnetic Force Between Current-Carrying Wires Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Jun 05, 2023

This magnetic force between current-carrying wires calculator lets you find the magnetic force between two parallel, long and straight wires carrying the current. Read the text below to learn why wires repel or attract each other and how you can estimate the strength of the electromagnetic force between them.

## Interaction between current-carrying wires

We describe the electric current flowing in the wire as an ordered movement of tiny charged particles - electrons. We know from Maxwell's equation that every moving charged particle produces a magnetic field. With our magnetic field of straight current-carrying wire calculator, you can check how strong a magnetic field can be created.

On the other hand, every moving charged particle in the magnetic field is subjected to the Lorentz force. Therefore, the magnetic field acts on the wire with current flowing through it too! Check out electromagnetic force on current-carrying wire calculator to estimate the force acting on that wire.

If one wire produces a magnetic field, the other feels it as an electromagnetic force. That's why two current-carrying cables interact with each other.

## Magnetic force between wires equation

A proper magnetic force calculation would require using the cross product, but there is a simpler way. The magnetic force between wires is straightforward to calculate if we assume that our wires are straight and very long. To estimate that force, you can use the following formula:

F / L = μ0 × Ia × Ib / (2 × π × d)

where

• Ia and Ib are the currents flowing in the first and the second wires;
• d is the distance between the wires;
• F / L is the force per unit length acting on each wire;
• μ0 is the permeability of free space which have constant value μ0 = 4 × π × 10^(-7) [T × m / A].

In many cases, we want to determine the force acting only on the selected wire section. For that reason, we have used the term F / L in the above equation. It means that if we have a wire with a length of L, it will be subjected to the force F.

## Attraction or repulsion?

So far, we have only said that two parallel current-carrying wires can interact with each other. But can we predict whether they will repel or attract each other? Yes, we can do it using our calculator! Current can flow through the wire in two directions. Let's indicate one with a positive value of I > 0 and the second with the negative I < 0.

If two wires are carrying current in the same direction, they attract each other (because F / L < 0), and they repel if the currents are opposite in direction (because F / L > 0). Moreover, due to Newton's third law, the force acting on the first wire must have the same magnitude as the force acting on the second wire.

Dominik Czernia, PhD
Current in first wire
A
Current in second wire
A
Distance
in
Force
N
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