# Lorentz Force Calculator

F = |q|·v·B·sinθ on a moving charge, with charge units down to elementary charges, speed and field selectors, and the v × B direction flipped for negative charges.

> Canonical page: https://elysiatools.com/en/tools/magnetic-force-charge

- **Category:** Science & Education

- **Keywords:** lorentz force, magnetic force charge, moving charge, cyclotron, v cross b, electromagnetism

## Overview

The Lorentz Force Calculator determines the magnetic force exerted on a moving electric charge using the formula F = |q|·v·B·sinθ. It supports charge inputs down to elementary charges (e), selectable velocity and magnetic field units (including Gauss and Tesla), and provides both force magnitude in Newtons and vector direction relative to the right-hand rule.

## Inputs

- **Charge q** (number): e.g. 1
- **Charge unit** (select)
- **Speed v** (number): e.g. 1
- **Speed unit** (select)
- **Magnetic field B** (number): e.g. 1
- **Field unit** (select)
- **Angle θ (degrees)** (number): e.g. 90

## When to use

- Determining the magnetic deflection force acting on charged particles such as electrons, protons, or ions.
- Analyzing beam trajectories and deflection parameters in cyclotrons, cathode-ray tubes, or mass spectrometers.
- Solving physics and electromagnetism problems requiring conversions between units like Gauss, microteslas, and elementary charges.

## How it works

- Enter the particle charge value and select the corresponding unit from Coulombs (C) down to elementary charges (e).
- Specify the particle speed and magnetic field strength with your preferred units (m/s, km/s, Tesla, Gauss, etc.).
- Set the angle θ in degrees between the particle velocity vector and the magnetic field lines.
- The tool evaluates F = |q|·v·B·sinθ to output the force magnitude in Newtons and indicates vector direction based on charge polarity.

## Use cases

- Beam physics calculations for bending ion trajectories in particle accelerators.
- Mass spectrometry calibration to predict ion deflection under known magnetic fields.
- Educational demonstrations illustrating the right-hand rule and angle-dependent force magnitude.

## Frequently asked questions

### What happens if a charged particle moves parallel to the magnetic field?

The magnetic force is zero because sin(0°) and sin(180°) equal zero.

### Why does a negative charge flip the force direction?

The vector force is defined as F = q(v × B); a negative sign inverts the resulting cross-product direction from the standard right-hand rule.

### Does the magnetic force change a particle's speed?

No. Because the magnetic force is always perpendicular to velocity, it does zero work and changes only trajectory direction, not speed.

### What is the relationship between Gauss and Tesla in this tool?

One Gauss (G) equals 10⁻⁴ Tesla (0.1 mT), which the calculator converts automatically.

### What value is used for one elementary charge (e)?

One elementary charge is evaluated as approximately 1.60218 × 10⁻¹⁹ Coulombs.

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