Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Maxwell's equation

Using the above definition of the potentials and applying it to the other two Maxwell's equations (the ones that are not automatically satisfied) results in a complicated differential equation that can be simplified using the Lorenz gauge where A is chosen to satisfy:

ablacdot extbf{A} + frac{1}{c^2} frac{partial phi}{partial t} = 0.

Using the Lorenz gauge, Maxwell's equations can be written compactly in terms of the magnetic vector potential A and the electric scalar potential ϕ:

abla^2phi - frac{1}{c^2}frac{partial^2 phi}{partial t^2} = - ho/ epsilon_0
abla^2 extbf{A} - frac{1}{c^2}frac{partial^2 extbf{A}}{partial t^2} = - mu_0 extbf{J}

In other gauges, the equations are different. A different notation to write these same equations (using four-vectors) is shown below.

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