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Related Concept Videos

Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Maxwell's Equation Of Electromagnetism01:29

Maxwell's Equation Of Electromagnetism

James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is represented by...
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...
Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of the problem,...

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Related Experiment Video

Updated: Jun 27, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Implicit high-order unconditionally stable complex envelope algorithm for solving the time-dependent Maxwell's

Shuqi Chen1, Weiping Zang, Axel Schülzgen

  • 1Photonics Center, College of Physics, Nankai University, Tianjin 300071, China.

Optics Letters
|November 28, 2008
PubMed
Summary
This summary is machine-generated.

We developed a new high-order algorithm for Maxwell's equations, offering unconditional stability and accuracy. This complex envelope method minimizes numerical errors for efficient electromagnetic simulations.

Related Experiment Videos

Last Updated: Jun 27, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Area of Science:

  • Computational Electromagnetics
  • Numerical Analysis
  • Applied Mathematics

Background:

  • Solving time-dependent Maxwell's equations is crucial for electromagnetic simulations.
  • Existing numerical methods often face challenges with stability and accuracy, especially at large time steps.
  • High-order methods are desired for improved simulation efficiency and reduced numerical errors.

Purpose of the Study:

  • To propose a novel implicit high-order algorithm for solving time-dependent Maxwell's equations.
  • To achieve unconditional numerical stability and high-order accuracy simultaneously.
  • To minimize numerical dispersion and dissipation in electromagnetic wave propagation simulations.

Main Methods:

  • Utilizing Padé approximation and a multistep method.
  • Developing an implicit, high-order, unconditionally stable complex envelope algorithm.
  • Comparing simulation results with exact solutions to validate the method's performance.

Main Results:

  • The proposed algorithm demonstrates unconditional numerical stability.
  • High-order accuracy in time is achieved.
  • The complex envelope formulation results in very small numerical dispersion and dissipation, even with large time steps.

Conclusions:

  • The developed algorithm provides an accurate and stable solution for time-dependent Maxwell's equations.
  • The complex envelope approach is effective in reducing numerical errors for electromagnetic simulations.
  • This method offers a promising tool for advanced computational electromagnetics research.