# Lorentz Force Calculator

Created by Krishna Nelaturu
Last updated: Oct 09, 2022

Our Lorentz force calculator will help you calculate the force exerted on charged particles moving through a magnetic field. If you're interested in understanding the effects of a magnetic field on charged particles, you've come to the right place! Here, we shall look at the Lorentz force law and an equation for the Lorentz force. We shall also look at some applications of Lorentz force.

If you're interested in the electromagnetic force between two charged particles, you should visit our Coulomb's law calculator.

## Lorentz force law

Lorentz's law describes the relationship between the electromagnetic force acting on a charged particle moving through electric and magnetic fields. The electromagnetic force is also known as Lorentz force in this instance. The equation for Lorentz force is given by:

$\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$

Where:

• $\mathbf{F}$ - The Lorentz force;
• $q$ - Charge of the charged particle;
• $\mathbf{E}$ - Electric field vector;
• $\mathbf{v}$ - Velocity of the charged particle; and
• $\mathbf{B}$ - Magnetic field vector.

Note that except for the charge $q$, all quantities are vector quantities - meaning they have a magnitude and direction. The term $q\mathbf{E}$ gives the electric force and the term $q(\mathbf{v} \times \mathbf{B})$ gives the magnetic force on the charged particle.

🔎 Some definitions only consider the magnetic force as Lorentz force. However, our Lorentz force calculator assumes the total electromagnetic force as Lorentz force. But don't fret - if you prefer only to calculate the magnetic half of this force, enter $0$ as the electric field strength, and you're good to go! ✌️

## Formula of Lorentz force magnitude

The formula for the magnitude of Lorentz force is:

$F = q(E + vB\sin\theta)$

Where:

• $E$ - Strength of the electric field;
• $v$ - Magnitude of the velocity of the charged particle;
• $B$ - Strength of the magnetic field; and
• $\theta$ - Angle between the particle's movement and the magnetic field.

This calculator uses this Lorentz force formula to calculate the Lorentz force. By default, the angle $\theta$ is set to $90 \degree$.

The Lorentz force is maximum when the initial path of the particle is perpendicular to the magnetic field, $\theta = 90\degree$. The magnetic term in the Lorentz force is zero when the initial path is parallel to the magnetic field.

Together with Maxwell equations, we can use the Lorentz force law to derive Faraday's law of electromagnetic induction.

## Applications of Lorentz force

The Lorentz force manifests in many electric devices. In particle physics, the Lorentz force accelerates charged particles in cyclotrons. It is also used in mass spectrometry of charged particles.

As a part of Laplace force, it occurs in many day-to-day devices such as electric motors and loudspeakers.

## How to use this Lorentz force calculator

Using our Lorentz force calculator is straightforward:

• Enter the charged particle's charge and initial velocity.
• Provide the strengths of the electric and magnetic fields.
• Input the angle between the initial path of the particle and the magnetic field. It is set to $90\degree$ by default, but you can change it if necessary.
• With this data, our tool will calculate the Lorentz force using the Lorentz force formula.
Krishna Nelaturu
Charge of the particle (q)
C
Velocity of the particle (v)
m/s
Electric field stength (E)
N/C
Magnetic field strength (B)
T
Angle (θ)
deg
Lorentz force
N
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