Lorentz Force Calculator

Created by Miłosz Panfil, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Aug 22, 2022

You can use this Lorentz Force Calculator to compute the effect of the magnetic field on charged particles. Reading the text, you will learn about the Lorentz force law, the corresponding Lorentz force equation, and about Lorentz force application in daily life.

Lorentz force law

The Lorentz force is a common effect of electric and magnetic fields acting on a charged particle. We will focus here only on the magnetic part of the force. For the electric part, you can check the Coulomb's law calculator.

The Lorentz force law states that a magnetic field exerts a force on a moving charged particle. The value of the force depends on the charge, the velocity, and the strength of the magnetic field.

What is a bit special is that the direction of the force is neither along the path of the particle motion nor the magnetic field. The direction of the Lorentz force is perpendicular to both the particle direction and to the magnetic field. As a result, the particle's trajectory bends in the magnetic field.

Also, the Lorentz force is zero if a particle moves precisely along the lines of the magnetic field. How can we write these observations in mathematical form? That's the Lorentz force equation.

Lorentz force equation

The Lorentz force equation is:

$\small F = qvB\sin(\alpha)$

where:

• $q$ – Particle's charge;
• $v$ – Particle's velocity;
• $B$ – Strength of the magnetic field;
• $α$ – Angle between the direction of the particle's trajectory and the direction of the magnetic field; and
• $F$ – Resulting force.

In our Lorentz force calculator, we set the angle α = 90° for simplicity. If you want to change it, go to the advanced mode. You can see that the force is maximal for that angle, and if we set α = 0°, it is also equal to 0.

Lorentz force applications

The Lorentz force finds applications in many areas. In science, it is used to accelerate particles in cyclotrons in the quest to find fundamental laws of particle physics. It is also used in mass spectrometers that allow for the identification of atoms and molecules.

Practical daily applications include electric motors, loudspeakers, and, likely less common among typical households, railguns.

Miłosz Panfil, PhD
Magnetic Field
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Charge
C
Velocity
m/s
Force
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