- #1

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- Homework Statement
- Refer to attached image

- Relevant Equations
- comlplex wave equation,

I am unsure of my solutions and am looking for some guidance.

a.)The real part of the wave in complex notation can be written as ##\widetilde{A} = A^{i\delta}##. Writing the Complex Wave equation, we have ##\vec E(t) = \widetilde{A}e^{(-kz-\Omega t)} \hat x##. Therefore the real part is ##\vec E(t) =Ae^{(-kz-\Omega t+\delta)} \hat x##. The negative in front of kz indicates it is a left traveling wave.

b.) The unit vector of ##\hat B = \frac{(\hat x - 2\hat z)}{\sqrt{5}}##. I know that ##\hat E## must be perpendicular to ##\hat B##, so simply,

##\hat E = \frac{(\hat x + 2\hat z)}{\sqrt{5}}##

c.) I am not so sure about this problem. I know that ##\vec E = \widetilde{E}_oe^{i(ky-wt)}\hat x##

Griffiths states ##\widetilde{B}_o = \widetilde{E}_o/c## and ##v=c/n##.

So ##\vec B = \frac{c\widetilde{E}_o}{1.7}e^{i(ky-wt)}\hat z##