Lecture

Maxwell's Equations: Derivation and Implications

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In course

PHYS-114: General physics : electromagnetism

Le cours traite des concepts de l'électromagnétisme, avec le support d'expériences. Les sujets traités inclus l'électrostatique, le courant électrique et circuits, la magnétostatique, l'induction électromagnétique, les équations de Maxwell, et les ondes él ...

Description

This lecture covers the derivation of the 4th Maxwell's equation, which relates the magnetic field to the current distribution. It explains the need for this equation to describe time-varying fields and introduces the concept of displacement current. The instructor demonstrates how the 4th Maxwell's equation is derived using Stokes' theorem and discusses its implications, such as the creation of magnetic fields by variable electric fields. The lecture also highlights the limitations of Ampère's circuital law and the significance of introducing the displacement current to ensure charge conservation. The Maxwell's equations are summarized, emphasizing their role in determining electric and magnetic forces based on charge and current distributions.

Instructors (3)

Lesya Shchutska

Current Work Our research is focused on testing the boundaries of the Standard Model of particle physics and on looking for new phenomena which might explain unanswered puzzles in the fundamental description of the Universe. The examples of such puzzles would be dark matter nature, matter-antimatter asymmetry of the Universe or very small but non-zero neutrino masses.The main instrument for these tasks is the LHCb detector at CERN, where the analyses of the data collected in the LHC proton-proton collisions

Fabio Avino

Education PhD in Physics | Turbulence at the boundary of toroidal plasmas with open and closed magnetic flux surfaces 2011 – 2015 EPFL Master in Physics | Rifrattometria su Plasmi di Interesse Termonucleare 2008 – 2010 La Sapienza Bachelor in Physics | Fluorescenza X portatile per l'analisi dei beni culturali 2005 – 2008 La Sapienza Professionals experiences Physicist - Senior Fellow 2017–2020 CERNScientist 2016–2017 EPFL Teaching & PhD P

Jan Hugo Dil

Teaching & PhD Past EPFL PhD Students Stefan Muff, Mauro Fanciulli, Fei Guo Courses Physics III PHYS-200 The students understand and apply the physics of fluids, and the basics of electromagnetism and electronic schemes Awards Latsis prize EPFL 2015 Heinrich Rohrer Rising Medal SSSJ 2014

Official source

Ontological neighbourhood

Physics

Electromagnetism: Electrodynamics

Related concepts (32)

Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets.

Electric field

An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field for a system of charged particles. Electric fields originate from electric charges and time-varying electric currents. Electric fields and magnetic fields are both manifestations of the electromagnetic field, one of the four fundamental interactions (also called forces) of nature.

Electromagnetic field

An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by moving electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified as light) and interacts with charges and currents.

Maxwell's equations

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar, etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields.

Ampère's circuital law

In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law) relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell (not Ampère) derived it using hydrodynamics in his 1861 published paper "" In 1865 he generalized the equation to apply to time-varying currents by adding the displacement current term, resulting in the modern form of the law, sometimes called the Ampère–Maxwell law, which is one of Maxwell's equations which form the basis of classical electromagnetism.

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