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I am working through chapter 47 of the Landau Lifschitz. And there is the following argument:

The vector potential is a function of [tex] t - \frac{x}{c} [/tex]

From the defining equations for the electric and magnetic fields:

[tex] \vec{E} = - \frac{1}{c} \frac{\partial \vec{A}}{\partial t}, \vec{B} = \nabla \times \vec{A} [/tex]

follows

[tex] \vec{E} = - \frac{1}{c} \vec{A'} [/tex]

[tex] \vec{B} = \nabla \times \vec{A} = \nabla (t- \frac{x}{c}) \times \vec{A'} = - \frac{1}{c} \vec{n} \times \vec{A'} [/tex]

[tex] \vec{B} = \vec{n} \times \vec{E} [/tex]

I can't follow his argument.

Why did the equation for the electric field change from a time derivative of A to a derivative over (t- x/c).

And where does that [tex] \nabla (t - x/c) [/tex] come from?

Finally where does that vector n come from?

Any help would be greatly appreciated!

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# Homework Help: Vectorpotential as a function of (t- x/c)

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