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    Untold secrets of the slowly charging capacitor

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    Author
    Milsom, John A.
    Affiliation
    Univ Arizona, Dept Phys
    Issue Date
    2020-02-20
    
    Metadata
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    Publisher
    AMER INST PHYSICS
    Citation
    Milsom, J. (2020). Untold secrets of the slowly charging capacitor. American Journal Of Physics, 88(3), 194-199. doi: 10.1119/10.0000635
    Journal
    AMERICAN JOURNAL OF PHYSICS
    Rights
    Copyright © 2020 American Association of Physics Teachers.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    The slowly charging capacitor is the standard example used to illustrate that the displacement current density is needed in Ampere's law if we want to correctly determine the magnetic field between capacitor plates. However, in any quasi-static situation the magnetic field can also be determined using the Biot-Savart law including only the real current densities. In this work, we will numerically calculate the magnetic field due to the surface currents on the capacitor plates and add it to the magnetic field due to the charging wire and show how they combine to create the correct magnetic field thoughout all space. For regions to the left or right of the capacitor, the space between the capacitor plates, we find the surprising result that the surface currents replicate the magnetic field that would have been created by the missing section of the charging wire between the plates. For points between the capacitor plates, the magnetic field due to the surface currents mostly cancels the magnetic field from the near-infinite length charging wire, resulting in the well-known reduced field in that interior region. We will also illustrate the impact of finite capacitor plates on these results and briefly comment on how textbook and/or classroom discussions could be improved by carefully discussing these details. (C) 2020 American Association of Physics Teachers.
    Note
    12 month embargo; published online: 20 February 2020
    ISSN
    0002-9505
    DOI
    10.1119/10.0000635
    Version
    Final published version
    ae974a485f413a2113503eed53cd6c53
    10.1119/10.0000635
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    UA Faculty Publications

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