Can a time-varying magnetic field emulate the electric field of a point charge?

  1. A point charge generates electric field lines that are radially directed from the source in spherical symmetry. Similarly, a line of charge generates electric field lines that are radially directed from the line of charge in cylindrical symmetry.

    Is there any way that a time-varying magnetic field generated by a time-varying current in a wire could emulate the electric field of an assemblage of static charges in the same geometry as the wire?

    I suppose the question may be geometry dependent. For a straight wire carrying DC steady current, the magnetic field is time-invariant and generates no electric field outside the wire.

    For the same wire carrying AC current with a single frequency, the magnetic field varies periodically and thus generates an electric field (though I have a hard time picturing the direction I believe that this induced electric field would be in the same direction as the original electric field ... parallel to the wire in this case).

    For an AC current that has 'higher order' changes in its frequency (i.e. - variation in the variation in electric field), there would be 'higher order' induced electric fields though again always in the same direction of the originally generating electric field in the wire.

    Therefore, I do not believe it is possible for a straight wire geometry to generate a radially-outward electric field by induction. Though, I cannot rule out that for other geometries of the current carrying wire that it is impossible. Does anyone have any insight on this?

  2. jcsd
  3. Drakkith

    Staff: Mentor

    You are asking if a magnetic field can emulate an electric field? If so, then the answer is no. The two are different effects and act differently.
  4. No, the electric field generated by time-varying magnetic field (vortex electric field) is distinct from that from charges (electrostatic field). The former has zero divergence while the latter has zero curl.
  5. Thanks for your reply Drakkith. No, I was referring to whether the induced electric field caused by a time-varying magnetic field could emulate the electric field of a static charge distribution.

    Thanks netheril, that is a very elegant way of answering my question and is a very helpful method for thinking about this!
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