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Electric field boundary equation implication at air/earth interface

  1. Sep 12, 2012 #1
    From an EM textbook (dealing with an above surface time varying magnetic field source):

    Primary field: Field artificially produced.
    Secondary field: Field produces by the charge/current created by the primary field.

    “Because air is so highly insulating in comparison to almost all in-situ earth materials, the conductivity contrast at the earth’s surface is virtually infinite… Since the normal component of total current density (conduction + displacement) must be continuous through a boundary, a charge distribution and a corresponding jump in the normal component of the electric field must occur there. The secondary electric field of the interface surface charge neutralizes most of the electric field that would otherwise exist within the earth, and it increases the electric field in the air. The only part of the electric field which continuous to be found in the earth is a circulation about the primary magnetic field lines which penetrate into the earth. A corollary of this reasoning is that an above-surface time varying magnetic source cannot produce an appreciable component of the electric field or current in a stratified earth normal to the layering”

    The bolded part is the part that I do not understand.

    My interpretation of the first part:

    Layer 1 (Dielectric, air, conductivity = s1 = 0) : Layer 2 (conductivity = s2)
    Jn1=Jn2 Current density continuation equation (n is the normal component)
    E1n*s1=E2n*s2 Ohms law
    0=E2n*s2 Since Jn1=0
    E2n=0 Since s2 =/= 0

    Thus an above surface time varying magnetic field source cannot produce an electric field normal to the boundary. Thus the electric field within this stratified earth will be purely tangential to the boundary.

    However, then it says that “the only part of the electric field which continuous to be found in the earth is a circulation about the primary magnetic field lines which penetrate into the earth”. I interpret this as Curl E = -dB/dt. But isn’t that the electric field were dealing with in the first place? The above ground time varying magnetic source produces the electric field via Curl E = -dB/dt. And surely it is not hard to imagine that Curl E = -dB/dt will produce an electric field that isn’t tangential to the boundary everywhere? Can anyone shed some physical meaning onto this for me? It seems as if they are talking about more than one electric field, one which circulates about the magnetic field lines (their time derivative) and then another which is having its normal component nullified.
     
  2. jcsd
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