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2: Introduction to Electrodynamics

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    • 2.1: Maxwell’s differential equations in the time domain
      This page explains Maxwell's equations, which describe the relationships between electric and magnetic fields through differential and integral forms. Key concepts like divergence and curl are introduced using the del operator (∇). Four fundamental equations govern electromagnetism, including Faraday's and Ampere's laws, while constitutive relations connect fields to material responses.
    • 2.2: Electromagnetic Waves in the Time Domain
      This page explains Maxwell's equations, which predict electromagnetic waves' existence and behavior in a vacuum using parameters like permittivity and permeability. It establishes that electric fields propagate perpendicular to their direction of travel, leading to polarization.
    • 2.3: Maxwell’s Equations, Waves, and Polarization in the Frequency Domain
      This page explores linear systems in relation to sinusoidal inputs, emphasizing wave manipulation through complex notation. It highlights the use of phasors in simplifying Maxwell's equations and deriving the Helmholtz wave equation. The relationship between phasor and time-domain expressions, governed by Faraday's law, is discussed alongside various polarization states, including linear and circular polarizations, and their representations.
    • 2.4: Relation between integral and differential forms of Maxwell’s equations
      This page explains Gauss's divergence theorem and Stokes' theorem, which connect vector fields' integral and differential forms. It outlines how these theorems are applied to convert Maxwell's equations between forms, detailing integral expressions for key laws like Faraday's and Ampere's. The text further includes practical examples demonstrating the use of Gauss's and Ampere's laws to calculate electric and magnetic fields, complemented by sketches to aid comprehension of Maxwell's equations.
    • 2.5: Electric and Magnetic Fields in Media
      This page covers Maxwell's equations and their application in describing electromagnetic waves and material properties, including conductivity in semiconductors and superconductivity. It addresses the impact of electric fields on dielectric materials, focusing on polarization and electric displacement. The page also explores magnetic permeability, its variations in materials, and the behavior of ferromagnetic substances, detailing concepts like magnetic saturation and hysteresis.
    • 2.6: Boundary conditions for electromagnetic fields
      This page explores Maxwell's equations relating to electromagnetic fields in materials, specifically focusing on boundary conditions at media interfaces. It details how these conditions influence perpendicular and parallel field components, the role of surface charges and currents, and the continuity required across boundaries.
    • 2.7: Power and Energy in the Time and Frequency Domains and the Poynting Theorem
      This page explores the Poynting theorem, which connects electric and magnetic fields to power and energy in electromagnetic systems. The text derives the theorem from Maxwell's equations, introduces the Poynting vector for power flow analysis, and explains the complexities associated with multiple frequencies and reactive power.
    • 2.8: Uniqueness Theorem
      This page explains the uniqueness theorem for Maxwell's equations, asserting that while multiple solutions may exist, specific boundary conditions can secure a unique solution.

    Thumbnail: The magnetic field of a current-bearing coil, illustrating field lines. (CC BY 4.0; Y. Qing).

    This page titled 2: Introduction to Electrodynamics is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David H. Staelin (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform.