- #1

lailola

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## Homework Statement

In the problem, the electric scalar and vector potentials are,

[itex]\phi=0, \vec{A}=A_0 e^{i(k_1 x-2k_2y-wt)}\vec{u_y}[/itex]

I have to find E, B and S.

Then, I have to calculate [itex]\phi '[/itex] that satisfies [itex]div\vec{A}+\frac{\partial \phi '}{\partial t}=0[/itex] Then calculate E and B.

Is it possible to find [itex]\vec{A}'[/itex] and [itex]\phi'[/itex] that satisfy the previous equation and produce the same E and B as [itex]\vec{A}[/itex] and [itex]\phi[/itex]?

## Homework Equations

[itex]\vec{E}=-grad\phi-\frac{\partial \vec{A}}{c\partial t}=0[/itex]

[itex]\vec{B}=rot(\vec{A})[/itex]

## The Attempt at a Solution

Using the equations I find:

[itex]\vec{E}=A_0wi/c e^{i(k_1x-2k_2y-wt)}\vec{u_y}[/itex]

[itex]\vec{B}=A_0ik_1 e^{i(k_1x-2k_2y-wt)}\vec{u_k}[/itex]

[itex]\vec{S}=\frac{c}{4\pi} \vec{E}x\vec{B}=1/(4\pi) A_0^2wk_1sin^2(k_1x-2k_2y-wt)\vec{u_x}[/itex]

For the next part I find,

[itex]\phi ' = - 2K_2 c A_0/(w) e^{i(k_1x-2k_2y-wt)}+ constant(x,y)[/itex]

Then, I calculate E and B as before.

I don't know how to answer the last part. Any idea?

Thank you.

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