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Maxwell equations in a vacuum

  • Thread starter SaveFerris
  • Start date
  • #1
1. Show that:

electric field E(x,t) = [0, Eo, 0] * f(kx-wt)

magnetic field B(x,t) = [0, 0, Bo] * f(kx-wt)

(where k, w, Eo, Bo are constants) satisfy the Maxwell equations in a vacuum where
charge and current densities are zero.

What relation between k and w must hold for a solution with Bo and Eo not equal to 0? How are Bo and Eo related in this case?


3. The Attempt at a Solution

I have finished the first part of this question proving that the Maxwell equations are solved, but am a little stuck on the second part!

i thought that if kx = wt then the equation would still equal zero, but as it's a function of kx-wt im not sure this works? if i could do that i thought finding k in terms of w might be the relationship but im not sure. this would give k = wt/x.

Thank you for any help!
 

Answers and Replies

  • #2
George Jones
Staff Emeritus
Science Advisor
Gold Member
7,312
859
What is, for example,

[tex]\frac{\partial B_z}{\partial t}?[/tex]
 

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