Magnetic Force on a Current-Carrying Wire Calculator

Creators

Dominik Czernia, PhD

Dominik Czernia

PhD, Institute of Nuclear Physics PAN

Website

Research Gate

Dominik Czernia, PhD, is a physicist at the Institute of Nuclear Physics in Kraków, specializing in condensed matter physics with a focus on molecular magnetism. He has led several national research projects, pioneering innovative approaches to novel materials for high technology. Passionate about making science accessible, Dominik has created various calculators, mostly in physics and math categories. In his free time, he enjoys family walks, city explorations, mountain hiking, and traveling everywhere by bike. See full profile

Check our editorial policy

Reviewers

Bogna Szyk and Steven Wooding

Steven Wooding

Steven Wooding is a physicist by training with a degree from the University of Surrey specializing in nuclear physics. He loves data analysis and computer programming. He has worked on exciting projects such as environmentally aware radar, using genetic algorithms to tune radar, and building the UK vaccine queue calculator. Steve is now the Editorial Quality Assurance Coordinator here at Omni Calculator, making sure every calculator meets the standards our users expect. In his spare time, he enjoys cycling, photography, wildlife watching, and long walks. See full profile

Check our editorial policy

New

With this magnetic force on a current-carrying wire calculator, you can estimate the magnetic force that 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 you can 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 that 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.

💡 To learn more about frictional forces, check out our friction calculator.

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 $\sin \alpha = 1$ . 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.