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1: Maxwell’s Equations

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    22719

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    • 1.1: Fundamental Postulates
      This page covers the properties of electrical charges, including their types, conservation, and interactions leading to electric and magnetic fields. Key concepts include superposition, Coulomb's law, and the forces on charged particles.
    • 1.2: Maxwell’s Equations
      This page explores the complexities of calculating electric and magnetic fields from charged particles in matter, emphasizing the importance of average fields in line with Maxwell's equations. It describes how neutral atoms produce no significant fields but can generate fields when subjected to external forces, resulting in dipole moments.
    • 1.3: Return to Maxwell’s Equations
      This page covers Maxwell's equations, a set of differential equations for calculating electric and magnetic fields using various coordinate systems. It highlights the need to perform essential calculations related to divergence and curl of vector fields. Key vector theorems, especially Gauss’ and Stokes’ Theorems, are emphasized for their relevance in relating surface integrals to volume properties, aiding in the solution of Maxwell's equations.
    • 1.4: The Auxiliary Fields D and H
      This page explains the rewriting of Maxwell's equations using two new vector fields, \(\vec D\) and \(\vec H\), in addition to the electric field \(\vec E\) and magnetic field \(\vec B\). It incorporates permittivity \(\epsilon_0\) and permeability \(\mu_0\), along with polarization \(\vec P\) and magnetization \(\vec M\), presenting a simplified version of Maxwell's equations that retains their physical significance while potentially aiding in memorization.
    • 1.5: The Force Density and Torque Density in Matter
      This page covers the impact of electric and magnetic fields on charged and polarized materials, focusing on force density and torque density concepts. It details how electric fields generate force densities linked to electric and magnetic dipole moments and includes relevant formulas. Additionally, it discusses the nabla operator's importance in field gradient calculations, enhancing the understanding of spatial variations in these fields.
    • 1.6: The CGS System of Units
      This page discusses the relevance of the CGS system in electricity and magnetism, particularly in displaying Maxwell's equations. It details the unit equivalence of electric and magnetic fields, auxiliary fields \(\vec D\) and \(\vec H\), along with conversion factors between CGS and MKS systems. Key ratios for charge and current densities are emphasized, and notable units for magnetic fields like Oersted and Gauss are mentioned.

    This page titled 1: Maxwell’s Equations is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by John F. Cochran and Bretislav Heinrich.