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Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

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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...
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Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

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Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
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Mass Analyzers: Common Types01:19

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The quadrupole mass analyzer consists of four cylindrical metal rods arranged in a diamond carrying a DC voltage and a radio-frequency AC voltage. The motion of ions through the quadrupole depends on the field strength, causing only ions of a certain m/z to resonate successfully and strike the detector at a given field strength. Though the transmission rate for these analyzers is high, the exact elemental composition of the sample is not determined because of low resolution; however, they are...
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Maxwell's Equation Of Electromagnetism01:29

Maxwell's Equation Of Electromagnetism

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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...
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Plane Electromagnetic Waves II01:29

Plane Electromagnetic Waves II

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Consider a plane wavefront traveling in position x-direction with a constant speed. This wavefront can be utilized to obtain the relationship between electric and magnetic fields with the help of Faraday's law.
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Gauss's Law: Cylindrical Symmetry01:20

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Related Experiment Video

Updated: Aug 30, 2025

Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing
09:39

Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing

Published on: June 28, 2024

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Quadraxial metamaterial.

D Sakhno, E Koreshin, P Belov

    Optics Letters
    |September 1, 2022
    PubMed
    Summary

    This study reveals that a specific metamaterial exhibits four unique optical axes below its artificial plasma frequency. These axes, independent of frequency, lead to the observation of conical refraction effects.

    Area of Science:

    • Electromagnetism and Metamaterials

    Background:

    • Investigating electromagnetic wave propagation in materials with spatially dependent properties is crucial for advanced optics.
    • Metamaterials offer unique electromagnetic responses not found in natural materials, necessitating detailed characterization.

    Purpose of the Study:

    • To analyze the dispersion of electromagnetic waves in a metamaterial with a Lorentz-like permittivity tensor.
    • To investigate the isofrequency contours and identify optical axes in a triple non-connected wire medium.

    Main Methods:

    • Analysis of isofrequency contours derived from the spatially dispersive permittivity tensor.
    • Mathematical modeling of electromagnetic wave propagation considering Lorentz-like dependence on the wave vector.

    Main Results:

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  • The metamaterial exhibits four distinct optical axes below the artificial plasma frequency.
  • The directions of these optical axes are frequency-independent and align with quadrant diagonals.
  • Conical refraction is observed for all identified optical axes.
  • Conclusions:

    • The studied metamaterial possesses unique optical properties characterized by multiple frequency-independent optical axes.
    • The findings demonstrate the potential for controlling electromagnetic wave behavior and observing phenomena like conical refraction in engineered metamaterials.