Question

an electromagnetic wave travels in xy plane making an angle theta with x axis.what is the equation of the wave?

Answer 1

Do you need real or complex expression?
Do you need both E and B fields?

Answer 2

both E and B

Answer 3

Well, the most interesting part is the phase of the wave.
Do you have an idea what it looks like?

Answer 4

If the wave had been travelling along the x-axis, its phase would have been:
\(\omega t-kx\) with \(k=\omega /c\)

Do you agree?

Answer 5

yes

Answer 6

Now this part \(kx\) is actually the dot product of wave vector \(\vec k\) and position \(\vec r=\vec{OM}\)

Hence: \(\omega t-\vec k .\vec r\) is the general expression.

Answer 7

okay..

Answer 8

So now... can you make up the right expression using your angle \(\theta\) ?

Answer 9

k vector is directed to positive x direction..and r vector makes an angle theta with X axis..so the dot product is krcos(theta)?

Answer 10

No, it is the other way round: \(\vec k\) is pointing at \(\theta\) with respect to the x-axis

whereas \(\vec r\) is any point (x,y,z) in space.

Answer 11

Remember \(\vec k\) represents the direction of the wave, like a ray of light does.

Answer 12

then the phase is k*x*cos(theta)+k*y*sin(theta)-wt..............?

Answer 13

Perfect!

You can leave k as it is or replace it with \(\omega /c\) if the wave is travelling in a vacuum.

Answer 14

ok...thank u...you are great sir.....please tell me a good modern physics book...

Answer 15

Sorry, I have no idea! I do not teach in English-speaking countries, so I do not know which books are good or not.
What level (what age) are you referring to?
I know one or two books for Relativity, but that's all I can do.

Answer 16

college level...i just passed high school...where are you from?

Answer 17

I am from France. What about you?

Answer 18

i am from India..do you teach in college?

Answer 19

Yes, I teach in 2nd year and I also teach teachers-in-training.

This book seems good (particularly the first chapters on special relativity):
Bernard Schutz, A first course in General Relativity, (Cambridge University Press).

Answer 20

thank you again sir....:)

Answer 21

yw :))