# Magnetic Force Between Current-Carrying Wires Calculator

By Dominik Czernia, PhD candidate
Last updated: Feb 22, 2019

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 do wires repel or attract each other at all and how can you estimate the strength of electromagnetic force between them.

## Interaction between current-carrying wires

Electric current flowing in the wire can be described 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 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 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 one feels it as the electromagnetic force. That's why two current-carrying cables interact with each other.

## Magnetic force between wires equation

A proper canlculation of the magnetic force would require the use of 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 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 in above equation, we have used the term F / L. 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 positive value I > 0 and the second with 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 first wire must have the same magnitude as the force acting on the second wire.

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