Lorentz Force
Force on charged particle in electromagnetic field
About Lorentz Force
The Lorentz Force represents force on charged particle in electromagnetic field. This physics formula is fundamental to mathematical analysis and serves as a cornerstone concept that students and professionals encounter throughout their mathematical journey. Its importance extends beyond pure mathematics into applied fields where quantitative analysis is required.
This formula is essential in Electromagnetism and Particle physics. It serves as a building block for more advanced mathematical theory and provides the foundation needed to understand complex mathematical relationships. Whether you're studying mathematics, physics, engineering, or economics, familiarity with this formula enhances your analytical capabilities.
Practical applications of the Lorentz Force include Particle physics, Electromagnetic devices, Plasma physics, among others. Understanding and correctly applying this formula enables problem-solvers to approach challenges more systematically and efficiently. Mastery of this concept not only expands your mathematical knowledge but also improves your overall quantitative reasoning skills.
Visual Preview
LaTeX Code
\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})Formula Information
Difficulty Level
Prerequisites
Discovered
19th century
Discoverer
Hendrik Lorentz
Real-World Applications
Examples
Mathematical Fields
Keywords
Related Topics
Important Notes
Total force on charged particle includes both electric and magnetic components.
Alternative Names
Common Usage
Formula Variations
Frequently Asked Questions
What is the Lorentz force?
The Lorentz force is the total force on a charged particle in an electromagnetic field: F = q(E + v × B), where q is charge, E is electric field, v is velocity, and B is magnetic field. It has two parts: electric force (qE) and magnetic force (qv × B). The magnetic force depends on velocity.
How does the electric force differ from magnetic force?
Electric force (qE) acts on any charged particle, regardless of motion, and is parallel to the electric field. Magnetic force (qv × B) only acts on moving charges, is perpendicular to both velocity and magnetic field (right-hand rule), and does no work (can't change kinetic energy, only direction).
What does the cross product mean?
v × B means the magnetic force is perpendicular to both velocity and magnetic field. Its magnitude is |F| = q|v||B|sin(θ), where θ is the angle between v and B. If v is parallel to B (θ = 0), magnetic force is zero. Maximum force occurs when v is perpendicular to B (θ = 90°).
What are practical applications?
The Lorentz force is used in: particle accelerators (guiding and accelerating charged particles), mass spectrometers (separating ions by mass), cathode ray tubes (deflecting electron beams), plasma physics (confining charged particles), and any device that uses electromagnetic fields to control charged particles.
How does this relate to Maxwell's equations?
Maxwell's equations describe how E and B fields are created. The Lorentz force describes how those fields affect charged particles. Together, they completely describe classical electromagnetism. The Lorentz force is the bridge between fields (E, B) and particle motion.
Why doesn't magnetic force do work?
Magnetic force is always perpendicular to velocity (F = qv × B), so F·v = 0. Since work W = F·d and power P = F·v, magnetic force does zero work. It can change direction but not speed. This is why magnetic fields can't accelerate particles - they only curve their paths.
Actions
Quick Details
- Category
- Physics
- Difficulty
- Advanced
- Discovered
- 19th century
- Discoverer
- Hendrik Lorentz
- Formula ID
- lorentz-force