how does a EM wave propagate in a medium?

That somebody is correct in say that EM wave can travel through vacuum because of its changing E-field and B-field.

Before i give you the explanation, it is necessary for you to understand the Lenz's Law and also the Right-Hand Screw Rule

(The following section highlighted in pink can be skipped)
[Lenz's Law]
It states that the direction of the induced emf is sich that it tends to oppose the flux change causing it, and does oppose it if induced currents flows. (You just only need to pay attention to the first part of this law)

[Right-Hand Screw Rule]
It states if a right-handed screw move forward in the direction of the (conventional) current, then the direction of rotation of the screw gives the direction of the magnetic field.

Now, suppose an EM wave is initiated by an oscillating electron in vacuum, the oscillating electron can be seem like a movement of charge-carrier inside a wire owing to the varying E-field, such that it produces a varying circular B-field . The direction of B-field can be found using Right-Hand Screw Rule. When we are looking at just a particular point in the space, there is a fluc change. By Lenz's Law, a B-field of the opposite direction is induced at that point, which can be seem part of another circular B-field (we call this induced circular B-field). Due to the influence of this induced circular B-field, the electrons inside this induced circular B-field will be driven to motion.

Up to this point, we may conclude that a primary oscillating electron in vacuum will initiate a secondary oscillating electron in vacuum. This story continues, and we conclude that an EM wave is propagated.

Note that all the changes are due to the varying E-field and B-field, which means it doesn't need any medium for propagation, which accounts for its propagation in vacuum.

I hope the above information helps
By 小儒

2007-07-26 18:19:52 補充：
Take it easy guy~ The above explanation is actually elaborated from a tutorial notes by Ken Chan. I think it has its value of reference =)

To explain the propagation of em wave in space, we need to apply Maxwell's equations. (Lenz's Law and Right Hand Screw Rule are not appropriate as they are not fundamental and they deal with electric current which is not found in space. Actually, in vacuum, there is certainly no electrons to be set in motion.)

The thrid or fourth Maxwell's equations in vacuum (i.e. without charges or currents) read as

curl (E) = - ∂B/∂t (1)
curl (B) = -(ε0/μ0)∂E/∂t (2)

(The curl of vector field tells us about the rotation the field has at any point. To have more information about curl, please visit http://en.wikipedia.org/wiki/Curl )

So, what Maxwell cleary indicated is "the extent of the rotation of E field is proportional to the rate of change of the B field at the same point in space".

Now assume the wave propagate in x-direction and the E field is in y-direction (i.e. E = E j)
Equation (1) simplifies to

∂E/∂x = -∂B/∂t where B = B k

So, when E field is at maximum, ∂E/∂x is zero, hence ∂B/∂t is zero and B is at maximum, too. When E field is at zero, ∂E/∂x is maximum, hence ∂B/∂t is at maximum and B is zero, too. Therefore, E and B field are in phase.