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2: Electrostatic Field I

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    22796

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    The Calculation of the Electrostatic Field Given a Time-independent Source Distribution.

    • 2.1: Introduction
      This page covers the electrostatic limit, which simplifies Maxwell's equations for stationary charge distributions. It explains how to calculate electric fields using superposition from charge distributions and highlights the roles of free charge density and dipole moment density in generating electrostatic fields and surface charges. Additionally, it addresses the complexities of calculating fields from point dipoles, especially near variations in dipole density at boundaries.
    • 2.2: The Scalar Potential Function
      This page covers the benefits of using a scalar potential function \(V(x,y,z)\) for deriving the electric field \(\vec E\) from charge distributions, simplifying the process compared to Coulomb's law. It explores how potential relates to charge densities and maintains finiteness despite divergences. Additionally, it discusses Poisson's equation and the Laplace operator, providing solutions for potential functions, including that of point dipoles, foundational for electrostatics.
    • 2.3: General Theorems
      This page outlines the applications of Gauss' Theorem in electromagnetism, focusing on Maxwell's equations. It details how to compute total charge using the divergence of the electric field and displacement vector, noting continuity at boundaries without free surface charges and addressing surface charge densities.
    • 2.4: The Tangential Components of E
      It follows from the first Maxwell equation, that the tangential components of the electric field vector must be continuous across any surface.
    • 2.5: A Conducting Body
      The electrostatic field must be zero inside a conducting body. A non-zero field would act on mobile charges in the body and so produce currents that would cause the charge distribution to change with time. Since the electrostatic field is zero everywhere inside a conducting body, it follows from that the electric field just outside a conducting body can have no components parallel with the surface.
    • 2.6: Continuity of the Potential Function
      This page discusses the necessity of continuity in the potential function to avoid unphysical infinite electric fields, highlighting that potential jumps can occur at dipole layers without generating external fields. It explains the relationship between dipole density and potential differences, particularly in electrical double layers found in cell membranes and at metal electrodes, emphasizing their significance in various natural phenomena, including battery operation.
    • 2.7: Example Problems
      This page covers electric fields and potential functions generated by various charge distributions, including uniformly charged infinite planes, polarized slabs, and ellipsoids. It highlights how electric fields behave in distinct regions, such as the uniform fields in double layers and the conditions under which fields remain constant or change direction.
    • 2.8: Appendix 2A
      This page describes two methods for calculating the potential function, V(\(\vec R\)), due to an electric dipole distribution, P(\(\vec r\)). The first method involves using the divergence of polarization to derive V from bound charges, while the second adds potentials from individual point dipoles. Both methods produce the same potential, differing only by a constant.

    Thumbnail: Field of a positive point charge influenced by a neutral conducting metal sphere. (CC BY-SA 3.0; Geek3 via Wikipedia)

    This page titled 2: Electrostatic 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 via source content that was edited to the style and standards of the LibreTexts platform.