How do you calculate Lorentz Magnetic Force?

Use the formula F = q × v × B × sin(θ). The magnetic part of the Lorentz force is the force on a charge moving through a magnetic field. Enter the values you know in the calculator above and it solves for the remaining variable.

What is the formula for Lorentz Magnetic Force?

The Lorentz Magnetic Force formula is F = q × v × B × sin(θ), where F—Magnetic force (N); q—Charge (C); v—Speed of the charge (m/s); B—Magnetic flux density (T); θ—Angle between velocity and field (degrees).

Lorentz Magnetic Force

F = q · v · B · sin(θ)

Calculator

Force

Charge

Velocity

Flux Density

Angle v to B

Result

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Formula

F = q × v × B × sin(θ)

Description

The magnetic part of the Lorentz force is the force on a charge moving through a magnetic field. It is maximum when the velocity is perpendicular to the field and zero when parallel. The force is always perpendicular to both the velocity and the field, which is why a uniform magnetic field makes charges move in circles rather than speeding them up. It underlies motors, Hall sensors, CRTs, and mass spectrometers.

Variables

F — Magnetic force (N)
q — Charge (C)
v — Speed of the charge (m/s)
B — Magnetic flux density (T)
θ — Angle between velocity and field (degrees)

Practical Notes

The full Lorentz force adds the electric term qE. Because the magnetic force does no work (it is perpendicular to motion), it changes direction but not the kinetic energy of the charge.

Related Concepts

All Fields & Electromagnetism formulas →

Coulomb’s Law Electric Field of a Point Charge Electric Potential of a Point Charge Gauss’s Law (Electric Flux) Lorentz Magnetic Force Force on a Current-Carrying Wire Force Between Parallel Wires Magnetic Field of a Straight Wire

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