Homework Help: Electromagnetic waves in a vacuum

1. Dec 10, 2003

scariari

show that electromagnetic waves in a vacuum are transversal waves.

transversal waves mean that the electric and magnetic wave fields are always perpendicular to each other and to the direction of the wave propogation... but how does this link to a vacuum? and how can you show that a field is perpendicular?

consider an electromagnetic plane wave and assume that it hits a boundary of a medium under a certain angle. assume that the dielectric constant, and magnetic permeability of the medium are given.
what are the boundary conditions on the electric and magentic fields at the boundary of the medium?
are there solutions for the plane waves that come in perpendicular to the boundary? (find them)

a plane wave is a wave travelling in the x-direction and has no y- or z- dependence. hitting a medium under a certain angle= a case of oblique incidence?
if the symbols were easier to type, i would write my answer, but to make sure, there are 4 boundary conditions for the case of it being parallel, in which #1 and #4 reduce to one common one and the third boundary condition also reduces.
for the case of it being perpendicular, it should have some connection with being parallel, but what? i assume that since the electric and magnetic fields are already perpendicular to one another, that there will only be two boundary conditions because not both the electric and the magnetic field can be perpendicular to this medium...

suppose that the medium would also contain a constant density of free electrons that respond to electric fields according to Ohm's law, describe the effect of the conduction electrons on the wave.

putting a free charge on a conductor makes it flow out to the edges. magnetic fields in a conductor lag behind the electric field, thus energy is not equally shared between the electric and magnetic fields. HELP!

2. Dec 11, 2003

arcnets

Vacuum means 'no charges and no currents'. You got to transform Maxwell's equations for this case into a wave equation. You will find the answer in a standard electrodynamics book, e.g. Jackson.
Maybe. This is all standard work (deriving things directly from Maxwell's equations) than can be found in the literature (or probably on the web...). Search for 'Fresnel's formulae'.
The reference to Ohm's law means that the body is not a perfect conductor in which charges can move with light speed. Instead, the current density will be proportional to the E-field strength. In what you say, you seem to refer to an induced current but that's not the case here.

3. Dec 12, 2003

scariari

sorry about the first post, i didnt include the whole problem: part a asks to derive the wave equation from Maxwell's equations. I did that no problem, but i guess question is
(from David J. Griffiths' "Introduction to Electrodynamics, chapter 8)

how does the fact that
curl.E =0 and
curl.B=0
show that electromagnetic waves are transverse?

(excuse the following confusing typing)
how does
-k(E0)x=w(B0)y
-k(e0)y=w(b0)x or

B0=k/w(ixE0)
show that E and B are mutually perpendicular?

4. Dec 12, 2003

scariari

about the second part, the boundary conditions at the boundary of the medium:

5. Dec 12, 2003

scariari

FIRSTLY, in the previous reply i used "CURL" instead of "del", my appologies...

about the second part of the original question, the boundary conditions at the boundary of the medium: i found 4 b.c's; for reflected perpendicular, transmitted perpendicular, reflected parallel, and transmitted parallel cases.

these are fresnel's equations.

this means that there are solutions for plane waves that come in perpendicular to the boundary, correct?

for oblique

reflected:
E0R=((n2 cos theta- n1 cos theta)/(n1 cos theta + n2 cos theta))E0I
transmitted:
E0T=((2n1 cos theta) /(n1 cos theta + n2 cos theta))E0I

for perpendicular
reflected:
E0R=((n1 cos theta- n2 cos theta)/(n1 cos theta + n2 cos theta))E0I
transmitted:
EOT=((2n1 cos theta) /(n1 cos theta + n2 cos theta))E0I