Calculating E Field from B Field of Monochromatic Plane Wave

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The discussion focuses on calculating the electric field (E) from the magnetic field (B) of a monochromatic plane wave, given the B field equation. Participants express confusion about the relationship between E and B, specifically questioning the formula E = -r x B in Gaussian units and its equivalent in SI units. There is a mention of needing to reference Griffiths' textbook for clarification on these equations. The conversation emphasizes the importance of understanding the derivation of these relationships rather than relying solely on provided formulas. Overall, the thread highlights the challenges of solving electromagnetic problems involving wave equations.
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Homework Statement


The B field of a monochromatic plane wave is

B~=B0~ exp(i(kz-wt)[sqrt(3)/2 x-hat + 1/2 y-hat]
Find E~ in terms of B0~.
and the polarization angle.


Homework Equations



We know E~=Eo~ exp(i(k.r-wt)nhat
B~=B0~ exp(i(k.r-wt)(k-hat x n-hat)

nhat = cos(theta)xhat + sin(theta)yhat

The Attempt at a Solution


Would have been trivial if given E instead of B.

What do I do?
 
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{\b E}=-{\hat r}\times{\b B} in gaussian units.
 
Where is this formula from? What is it in SI?

B= 1/c script r x E is true, i don't know about E = script r x B, where did u get this fomrula? Where is it in griffith if it is?
 
Last edited:
Do kXB in (9.49). You have to learn to do some things for yourself.
 
(a) The polarisation pattern is elliptical with maximum (1,1) and minimum (-1,-1), and anticlockwise in direction. (b) I know the solution is a quarter-wave plate oriented π/4, and half-wave plate at π/16, but don't understand how to reach there. I've obtained the polarisation vector (cos π/8, isin π/8) so far. I can't find much online guidance or textbook material working through this topic, so I'd appreciate any help I can get. Also, if anyone could let me know where I can get more...

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