# Magnetic Force Between Current-Carrying Wires Calculator

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.

Keep reading to learn more!

## 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:

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.