Electromagnetic Force on Current-Carrying Wire Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Oct 20, 2022

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 the moving electrons (which comprise the current) will experience the Lorentz force (see our Lorentz force calculator for more details). It means that this wire will start moving if there is no other strong enough force that can stop it, for example, a friction force. Such a condition may be met when the wire hangs vertically in the air.

Magnetic force on straight current-carrying wire equation

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

$F = BIl\sin\alpha,$

where:

• $B$ – Strength of magnetic field;
• $I$ – Current flowing through the wire;
• $l$ – Length of the wire; and
• $\alpha$ – Angle between the direction of current and the direction of the magnetic field.

We assumed for simplicity that $\alpha = 90\degree$ and therefore $\sin \alpha = 1$. 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 ($\alpha = 0$), the resulting force is zero. On the other hand, the highest possible electromagnetic force is achievable when those directions are perpendicular ($\alpha = 90\degree$).

What next?

Did you know that a current-carrying wire produces a 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 carrying current near each other, which creates a magnetic field. 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
Magnetic field
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Current
A
Length
ft
Force
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