# Magnetic Force Between Current-Carrying Wires Calculator

Created by Luciano Mino
Last updated: Jul 08, 2022

The magnetic force between current-carrying wires calculator will obtain the magnitude of the magnetic force that appears when current flows through two wires that are close to each other.

Within a few paragraphs, you will learn why this phenomenon appears and how to calculate the magnitude of the magnetic force. We will also show you how you can quickly identify if the force between the wires is attractive or repulsive.

## Why is there a force between two parallel wires?

First, we should address why this counter-intuitive phenomenon occurs.

As we know, when current flows through a straight wire, an induced magnetic field appears, and we can find its direction using the right-hand rule.

We also know that if a charge moves through a magnetic field, it will experience a force (the Lorentz force).

Suppose we have one current-carrying wire inducing a magnetic field and then place another current-carrying wire close enough to be affected by this induced magnetic field.

As we described before, the charges moving within the second wire will experience a force, which will bring the cables closer together or further apart.

💡 If you're already familiar with this topic, feel free to start using the magnetic force between current-carrying wires calculator right away! Otherwise, check our magnetic Field of Straight Current-Carrying Wire and magnetic Force on Current-Carrying Wire calculators!

## How to calculate the magnitude of the force between two parallel wires

We can easily find the force per unit length on acting on each wire with the following formula:

$\frac{F}{L} = \frac{\mu_{0} I_{a} I_{b}}{2 \pi d}$

where:

• $m_{0}$ is the permeability of free space, which is a constant;
• $I_{a}$ is the current flowing through one of the wires;
• $I_{b}$ is the current flowing through the other wire; and
• $d$ is the distance between the wires.

🙋 While this equation seems complicated, it is not! You only need three parameters to find the force acting on the wires. Replace these parameters in the magnetic force between current-carrying wires calculator, and it will automatically find this value for you!

## Is the force between the wires attractive or repulsive?

We can also find if the force is attractive or repulsive using the magnetic force between current-carrying wires calculator.

The right-hand rule first tells us the direction of the induced magnetic field and then the direction of the force when we're calculating the Lorentz force.

We can also obtain the direction from the previous equation:

• If the current flows in the same direction on both wires, the force is positive, which causes the wires to repel each other.
• Otherwise, the force will be negative if the current flows in opposite ways on each wire. This causes an attractive force, bringing the wires closer together.
Luciano Mino
Current in first wire
A
Current in second wire
A
Distance
in
Force
N
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