# Lorentz Force Calculator

Created by Miłosz Panfil, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Dec 27, 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 out our 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.

## FAQ

### How do I calculate the Lorentz force?

To calculate the Lorentz force, follow these easy steps:

1. Measure the charge of the particle q in coulomb.
2. Measure the intensity of the magnetic field B in tesla.
3. Find the velocity of the particle v in meters per second.
4. Calculate the angle α between the particle's trajectory and the magnetic field.
5. Multiply these values through the formula to get the Lorentz force:
F= q × v × B × sin(α).

### How do I find the direction of the deflection due to the Lorentz force?

The direction of the deflection due to the Lorentz force depends on the relative angle between the particle's trajectory and the direction of the magnetic field in which the particle it's moving.

For a positively charged particle:

1. Align your right thumb with the particle's speed.
2. Align the right index finger with the magnetic field.
3. Extending your right middle finger perpendicular to the plane created by the other gives the direction of Lorentz force.

When dealing with negative particles, invert the direction of the force.

### What is the Lorentz force on an electron moving in a 0.5 T field at 0.1 c?

The force is 2.402e-12 N. To find this result, use the following data:

• q = 1×e = 1.602e-19 C.
• B = 0.5 T.
• v = 0.1 c = 2.998e7 m/s

We assume α = 90°. Use the formula for The Lorentz force:
F = q × v × B × sin(90°)
F = 1.602e-19 C × 0.5 T × 2.998e7 m/s
F = 2.402e-12 N.

### Where can I find the Lorentz force?

The Lorentz force appears wherever a charged particle moves in a magnetic field: you can measure it in electric wires, for example, but most importantly in machines like cyclotrons and synchrotrons, where the magnetic field deviates the particle on a spiraling or circular trajectory. Physicists also use the Lorentz force in cosmic rays detectors, where thanks to different trajectories, it is possible to identify the various types of particles in the sensor.

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