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SaveFerris
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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 I am not sure this works? if i could do that i thought finding k in terms of w might be the relationship but I am not sure. this would give k = wt/x.
Thank you for any help!
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 I am not sure this works? if i could do that i thought finding k in terms of w might be the relationship but I am not sure. this would give k = wt/x.
Thank you for any help!
