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Maxwell Equations in Tensor Notation

  1. Jun 5, 2012 #1
    2A[itex]\mu[/itex]=-[itex]\mu[/itex]oJ[itex]\mu[/itex]

    Griffith's Introduction to Electrodynamics refers to this 4-vector equation as "the most elegant (and the simplest) formulation of Maxwell's equations." But does this encapsulate the homogeneous Maxwell Equations? I see how the temporal components lead to Gauss' Law, and I'm assuming, though I haven't shown it to myself, that the spatial components lead to the Ampere-Maxwell Law. What about Faraday's Law and the divergence of B?
     
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  3. Jun 5, 2012 #2

    Matterwave

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    The other two laws are basically obtained by definition of the E and B fields. For example, by defining B as the curl of a vector potential, it is then divergence-less by definition.

    I would say that the "most elegant" way to formulate Maxwell's equations is by using the Faraday tensor ([itex]F\equiv dA[/itex], where d is the exterior derivative) :

    [tex]dF=0[/tex]

    [tex]d*F=4\pi*J[/tex]

    But this requires a little bit of differential geometry to understand.
     
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