Calculating the Magnetic Field & Poynting Vector of Light

[fluidistic]

Homework Statement

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?

Homework Equations

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

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?

 

[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).

 

[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

 

[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?

 

[paranormal]

I can provide some guidance and equations to help you solve this problem. First, you are correct in thinking that Maxwell's equations are relevant here. Specifically, the equation you mentioned, \frac{\partial B}{\partial t}=-c \vec \nabla \times \vec E, is known as the Maxwell-Faraday equation. This equation describes the relationship between the time rate of change of the magnetic field and the curl of the electric field.

To solve for the amplitude of the magnetic field, we can use the fact that in a vacuum, the speed of light is equal to the product of the electric and magnetic field amplitudes (c = E_0*B_0). This relationship can be extended to different mediums by using the refractive index (n) of the medium. In this case, we can write B_0 = E_0/(n*c).

To find the magnitude of the Poynting vector, we can use the equation you mentioned, \vec S = \vec E \times \vec H. This equation represents the direction and magnitude of the energy flow of an electromagnetic wave. In this case, we can use the amplitude of the electric and magnetic fields to calculate the magnitude of the Poynting vector.

To fully solve this problem, you will need to use the equations above and also consider the direction and polarization of the wave. I encourage you to review these equations and try to solve the problem on your own. If you need further help, you can consult with your instructor or a colleague.