Lorentz force

Lorentz force on charged particles in bubble chamber - HD.6D.635 (12000265314)

Lorentz force particle

Lorentz force continuum

H. A. Lorentz - Lorentz force, div E = ρ, div B = 0 - La théorie electromagnétique de Maxwell et son application aux corps mouvants, Archives néerlandaises, 1892 - p 451 - Eq. I, II, III

charged-particle-drifts

Regla mano derecha Laplace

Lorentz Force is a fundamental concept in electromagnetism that describes the force exerted on a charged particle moving through an electric field and a magnetic field. Named after the Dutch physicist Hendrik Lorentz who formulated it in 1895, the Lorentz force is pivotal in understanding and analyzing the motion of charged particles in electromagnetic fields, and it plays a crucial role in the fields of physics, electrical engineering, and many applied sciences.

Definition

The Lorentz force can be mathematically expressed as:

F = q(E + v × B)

where:

• F is the force applied to the particle (in newtons, N)
• q is the electric charge of the particle (in coulombs, C)
• E is the electric field (in volts per meter, V/m)
• v is the velocity of the particle (in meters per second, m/s)
• B is the magnetic field (in teslas, T)
• × denotes the cross product

This equation implies that the force exerted on a charged particle is dependent on its charge, its velocity, the electric field present, and the magnetic field present. The direction of the force is perpendicular to both the velocity of the particle and the magnetic field, as determined by the right-hand rule.

Applications

The Lorentz force law is fundamental in the design and operation of many devices and technologies such as electric motors, particle accelerators, cathode ray tubes, and magnetic resonance imaging (MRI). It is also essential in the study of phenomena such as the Aurora Borealis, where charged particles from the sun interact with the Earth's magnetic field.

History

The concept of the Lorentz force predates its formal definition by Hendrik Lorentz. Early experiments by Michael Faraday, André-Marie Ampère, and others hinted at the underlying principles of electromagnetic force. However, it was Lorentz's work that systematically described the force acting on a charged particle in both electric and magnetic fields, integrating the work of James Clerk Maxwell and others into a coherent theory of electromagnetism.

See Also

• Electromagnetic field
• Maxwell's equations
• Electromagnetic induction
• Hall effect

Further Reading

For those interested in a deeper understanding of the Lorentz force and its implications in physics and engineering, further exploration into electromagnetism, classical mechanics, and quantum mechanics is recommended. Texts on electrical engineering and particle physics also provide extensive applications and examples of the Lorentz force in action.