Electromagnetic waves and vector calculus

[Pingu]

I'm having trouble with electromagnetic waves, perhaps just a vector calculus issue. I'd much appreciate some help in idenfiying it.

If given say an example in an assignment of an electromagnetic wave:

E = E_0 cos (omega(sqrt(sigma.mu) z - t )) X
+ E_0 sin (omega(sqrt(sigma.mu) z - t )) Y

Where bold X & Y have hats on their heads :-D

If so , what is the vector B
I'd immediatley assume that it was the same equation, replaced with B_O's instead of E_0's and swapping the cos's with sins's or the X & Y's.

Simplistic assumption based on the two assumably being mutuall perpendicular and in phase.

That would lead me to be able to identify the poynting vector S
I'm wondering if it is the same solution as a monochromatic plane wave, and furthermore what relationship the magnetic energy density and the electric energy density have, over a suitable averaging.

Thanks for reading, and if you have anything to comment, i'd love to hear it. I'm reading from Griffith Intro to Electro chapter 9 to attempt understanding...

Cheers
Andy :-D

 

[siddharth]

I'm having trouble with electromagnetic waves, perhaps just a vector calculus issue. I'd much appreciate some help in idenfiying it.

If given say an example in an assignment of an electromagnetic wave:

E = E_0 cos (omega(sqrt(sigma.mu) z - t )) X
+ E_0 sin (omega(sqrt(sigma.mu) z - t )) Y

Where bold X & Y have hats on their heads :-D

If so , what is the vector B
I'd immediatley assume that it was the same equation, replaced with B_O's instead of E_0's and swapping the cos's with sins's or the X & Y's.

That's not right. Remember that $\vec{E}$ satisfies Maxwell's equations. So, what do the first 2 equations in vacuum tell you? From this, can you find the magnetic field?