Lorentz Force Calculator

Lorentz Force Calculator | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Science & Education
Input types: number, select
Output type: text
Sample coverage: 4
API ready: Yes

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.

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

1Enter the particle charge value and select the corresponding unit from Coulombs (C) down to elementary charges (e).
2Specify the particle speed and magnetic field strength with your preferred units (m/s, km/s, Tesla, Gauss, etc.).
3Set the angle θ in degrees between the particle velocity vector and the magnetic field lines.
4The 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.

Examples

1. Electron Deflection in a Millitesla Field

Physics Student

Background

An undergraduate lab experiment investigates electron beam curving inside a cathode-ray tube subject to a uniform perpendicular magnetic field.

Problem

Calculate the instantaneous magnetic force acting on an electron moving at 1,000,000 m/s perpendicular to a 1 mT field.

How to use

Set Charge q to -1 with unit 'e', Speed v to 1000000 m/s, Magnetic field B to 1 mT, and Angle θ to 90°.

Outcome

Calculates a force magnitude of 1.60218×10⁻¹⁶ N directed opposite to v × B due to the negative charge.

2. Standard Reference Case

Physics Instructor

Background

An instructor needs a clean unit baseline to demonstrate the fundamental definition of the Tesla in SI units.

Problem

Demonstrate the force on a 1 Coulomb charge moving at 1 m/s perpendicular to a 1 Tesla field.

How to use

Enter Charge q = 1 C, Speed v = 1 m/s, Magnetic field B = 1 T, and Angle θ = 90°.

Outcome

Yields an exact force magnitude of 1 N directed along v × B according to the standard right-hand rule.

FAQ

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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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Electron Deflection in a Millitesla Field

2. Standard Reference Case

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