# Light, EM wave

1. May 5, 2010

### fluidistic

1. The problem statement, all variables and given/known data
If the amplitude of the electric field of the light propagating through a glass whose refractive index is 1.5 is 100 V/m, what is the amplitude of the magnetic field?
What is the magnitude of the Poynting vector associated with this wave?

2. Relevant equations
Not sure for the first question and the second is $$\vec E \times \vec H$$ if if I remember well.

3. The attempt at a solution
So the second question is easily answered when I know what is the worth the magnetic field. I really don't know any equation that relates the E field and the B field of a wave.
Maybe Maxwell's equation? This one in particular (using Gaussian units): $$\frac{\partial B}{\partial t}=-c \vec \nabla \times \vec E$$.
Or maybe I should write the solution to the wave equation of the light in the medium?
I'm not really sure how it would be. $$E(x,t)=E_0 \cos (\omega t + \vec k \cdot \vec x )$$ or something like that, I'm not sure.
That's a good problem, I wasn't aware one could get the B field from the E field in the wave of light.
Any tip?

2. May 5, 2010

### mooglue

It might be something simple like that given an EM wave in a medium of index of refraction n, you can use

B(w,r) x ek = n(w) E(w,r).

3. May 5, 2010

### mooglue

And yes, you wrote the correct expression for the poynting vector. In a medium like that, the waves are still going to be perpendicular. It's really only in a waveguide and other special circumstances that this is not the case, so you can just use that the magnitude of the pointing vector is proportional to E^2 H^2

4. May 5, 2010

### fluidistic

Ok thanks a lot for the replies.
Could you precise what are the variables w, r and e in the expression "B(w,r) x ek = n(w) E(w,r). "?
I'm guessing that k is a vector pointing in the sense of propagation of the wave. Also I never seen such an equation. Do you know a book in which the derivation is done?

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