Magnetic field
T
Current
A
Length
ft
Force
N

# Electromagnetic Force on Current-Carrying Wire

By Dominik Czernia, PhD candidate

With this electromagnetic force on current-carrying wire calculator, you can estimate the magnetic force which acts on the straight wire with current flowing through it. From a microscopic point of view, the electric current is the result of the flow of tiny charged particles - electrons. If the charged particle moves in a magnetic field, it will be subjected to the Lorentz Force. In the text below we explain how can you estimate the force acting on a straight wire with about 1012 electrons moving through it.

## When can we observe electromagnetic force?

When we place a wire which carries the electric current in the magnetic field, each of moving electrons (which comprise the current) will experience the Lorentz Force. It means that this wire will start moving if there is no other strong enough force which can stop it, for example a friction force. Such condition may be met when the wire is hanging vertically in the air.

## Magnetic force on straight current-carrying wire equation

Making use of some mathematical tricks to avoid using the cross product, we can simplify the formula. The formula that lets you calculate the strength of magnetic force acting on the straight current-carrying wire is simple:

`F = I * B * L * sin(α)`

where

• `I` is the current flowing through the wire;
• `B` is the strength of magnetic field;
• `L` is the length of the wire;
• `α` is the angle between the direction of current and the direction of the magnetic field.

We assumed for simplicity that `α = 90°` and therefore `sin(α) = 1`.You can go to advanced mode if you want to change this angle too. From this formula, you can see that if the directions of the current and magnetic field are parallel (`α = 0`), the resulting force is zero. On the other hand, the highest possible electromagnetic force is achievable when those directions are perpendicular (`α = 90°`).

## What next?

Did you know that the current-carrying wire produces its magnetic field? You can read more about it and determine the strength of this magnetic field with our magnetic field of straight current-carrying wire calculator. Now imagine that there are two wires with current near each other which will create their magnetic fields. What do you think will happen to them? If you are curious, you can find this answer with our magnetic force between current-carrying wires calculator.

Dominik Czernia, PhD candidate