# Question on EM wave in space and matters.

1. Jun 29, 2011

### yungman

My understanding from the book about EM wave that E and B is perpendicular to the direction of propagation only in medium that is charge free so $\nabla \cdot \vec E = 0$. What cases when E and B not perpendicular to the direction of propagation?

Thanks

Alan

2. Jun 29, 2011

### chrisbaird

Inside a waveguide, on the surface of a conductor, in the near-field of a radiating source such as an antenna, in evanescent waves.

3. Jun 29, 2011

### yungman

Thanks for the response, I forgot to mention the source is from far distance so the wave front approx a plane.

So as long as it is charge free homogeneous medium, E and B always perpendicular to direction of propagation?

At surface of conductor or in waveguide, that is surface charge, so the medium( the boundary) is not charge free. How is the E and B relate to direction of propagation and to each other?

Thanks

Alan

4. Jun 30, 2011

### yungman

I was thinking about the waveguide, a parallel plate transmission line is a waveguide, but the E and B are perpendicular to each other and normal to the direction of propagation.

5. Jun 30, 2011

### chrisbaird

Yes, in free space (far away from any kind of charges or currents), traveling electromagnetic waves can only exist as transverse waves. You can show this by taking the source-less divergence equations from Maxwell's equations, and assuming a traveling wave form. You can have electromagnetic fields that are not perpendicular if we are not talking about traveling waves. Place a magnet next to a charged sphere and in the free space near them you can get just about any alignment of the electric field relative to the magnetic field, depending how you position the magnet and sphere.

In a waveguide, the direction of propagation is down the waveguide. E and B are still mutually perpendicular, but they are not both necessarily perpendicular to the direction of propagation. One of them will have an axial component (except for in the TEM mode).

On the surface of a good conductor, the E field is perpendicular to the surface, the B field is parallel, and the direction of propagation is in general at some oblique angle.

In the near-field of radiating sources, things can get very complicated and there is no standard alignment of the E and B fields.

In evanescent waves, for p-polarized light incident on a dielectric interface, the direction of propagation is along the interface and in the plane of incidence, the magnetic field is along the interface and normal to the plane of incidence, but the electric field has components normal to the interface but also in the direction of propagation. Again, E and B are perpendicular, but one has a component in the direction of propagation.

6. Jun 30, 2011

### yungman

Thanks

Let me study through this first.

7. Jul 1, 2011

### RedX

If you orient the sphere and magnet such that ExB is nonzero, is there a Poynting flux with static fields?