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4: The Magnetostatic Field I

  • Page ID
    22817
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    The Calculation of Magnetic Fields Given a Time-independent Distribution of Sources.

    • 4.1: Introduction
      This page elaborates on Maxwell's equations under static conditions, illustrating the separation of electric and magnetic fields. It emphasizes the role of the vector potential \(\vec{A}\) in defining magnetic fields and current densities.
    • 4.2: The Law of Biot-Savart
      This page covers current density in thin wires, detailing the calculation of current density as total current over cross-sectional area. It derives the Biot-Savart law for the magnetic field generated by electric currents and explains how moving charge carriers create magnetic fields, contrasting with stationary charges. The discussion includes detailed mathematical formulations of these concepts.
    • 4.3: Standard Problems
      This page covers the analysis of magnetic fields and vector potentials generated by various current configurations, including a straight wire, solenoid, and current loops. It derives vector potentials in cylindrical and spherical coordinates, applies Stokes' theorem for simplification, and discusses the uniform magnetic field inside an infinite solenoid.
    • 4.4: A Second Approach to Magnetostatics
      This page covers key aspects of magnetostatics, emphasizing the derivation and implications of Maxwell's equations. It explores the relationships between magnetic fields and current density, introduces magnetic charge density, and uses magnetic scalar potential to calculate fields. The transformation of volume to surface integrals in magnetized objects and the derivation of fields from point dipoles are discussed, highlighting parallels with electrostatics.

    Thumbnail: Magnetic B-field inside and outside of a cylindrical bar magnet. (CC BY-SA 4.0 International; Geek3 via Wikipedia)


    This page titled 4: The Magnetostatic Field I is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by John F. Cochran and Bretislav Heinrich.