Verifying Answer to Wave Equation and Associated B Field

[Hoofbeat]

Hi, I have the following question on my problem sheet, and I just want to check that my answer to it is correct as I need to use the result in a later problem. If someone could confirm it is correct, or point out mistakes/erros that would be great.

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Q. Derive the wave equation for E in empty space (Form the curl of Maxwell II and use a vector identity.). Find the condition that the plane wave E = eyEycos(wt - kx) is a solution (k=2pi/lamda). Use Maxwell II to find the B field associated with this electric field.
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A. I've done the derivation fine to get:

Laplacian E = epsilon-0.mu-0. d^2E/dt^2 [these are partial derivatives]

this is the same as d^2E/dx^2 = (1/c^2).(d^2E/dt^2) which can be solved using separation of variables to get E = eyEycos(wt - kx).

To find the associated B field, we used Maxwell II, ie. curlE = -dB/dt.

CurlE = -keyEysin(wt - kx)

B = integral - [curl E] dt

B = k/w. eyEycos(wt - kx)

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Thanks

 

[dextercioby]

$$\vec{B}=-\int dt \nabla\times\vec{E}$$

What is the curl of $\vec{E}$...?And then evaluate the integral correctly.

Daniel.

 

[Hoofbeat]

$$\vec{B}=-\int dt \nabla\times\vec{E}$$

What is the curl of $\vec{E}$...?And then evaluate the integral correctly.

Daniel.

Isn't the curl of E in this case, just the value of E calculated earlier, integrated wrt x?

 

[dextercioby]

That curl is a vector and should have 2 components,namely on $Ox_{1}$ and $Ox_{3}$ axis of coordinates...

So it's incorrect what you have written.Please do the calculations again.

Daniel.