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Redundant cross product removed from Maxwell equation?

  1. Aug 27, 2008 #1
    I'm trying to track down the rationale for removing the cross product of velocity and magnetic field intensity from Maxwell's equation which specifies the value of the electric field intensity. In the third edition of "A Treatise on Electricity and Magnetism" Maxwell specifies (in modern terminology) that E = cross product of velocity and B minus the derivative with respect to time of the vector potential minus the gradiant of the scalar potential.

    Was the assumption that the potential already contains the changing value of the magnetic field so that the cross product is redundant? It seems that Maxwell was second-guessed when Gibbs and Heaviside developed the modern variant of the equations.
  2. jcsd
  3. Aug 28, 2008 #2
    The equation intended by Maxwell is: [itex] E= v [/itex] x [itex] B - dA/dt - \nabla \phi [/itex]
  4. Aug 28, 2008 #3


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    I think you're referring to the Lorentz force equation, where q=1C:

    If Wikipedia is to be believed, this paragraph addresses your concerns:
    Last edited by a moderator: May 3, 2017
  5. Aug 28, 2008 #4
    Yes, that's exactly what I was referring to. Thanks for the reference.

    Maxwell says that the [itex] v [/itex] x [itex] B [/itex] term is only needed when the particle is moving in a magnetic field. Otherwise the equation is the same as the modern equation for the E field defined with respect to the potentials I believe. Seems to be a mystery how to interpret what Maxwell was thinking and further study seems warranted.
  6. Aug 28, 2008 #5


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    This is a good reason why I don't bother reading original papers. Apart from the fact that their notation is outdated, the authors are often wedded to the the prevailing paradigms of their time, which may end up confusing the reader.
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