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Hi,

I have two questions about the solutions to Maxwell’s wave equations:

1. I always hear that E and B must be in phase. Why is this, mathematically? And wouldn’t this also be a solution:

B

E

In which case E and B are out of phase.

2. In a vacuum with no charges or currents, would all solutions of Maxwell’s equations (including super positions of plane waves) involve E and B being perpendicular to each other? Also, on a related note, in the case of no charges or currents, do all solutions have to be superpositions of plane waves?

Thanks in advance!

I have two questions about the solutions to Maxwell’s wave equations:

1. I always hear that E and B must be in phase. Why is this, mathematically? And wouldn’t this also be a solution:

B

_{y}=B_{0}sin(kz)cos(wt)E

_{x}=E_{0}cos(kz)sin(wt)In which case E and B are out of phase.

2. In a vacuum with no charges or currents, would all solutions of Maxwell’s equations (including super positions of plane waves) involve E and B being perpendicular to each other? Also, on a related note, in the case of no charges or currents, do all solutions have to be superpositions of plane waves?

Thanks in advance!

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