In a sourceless and loseless region an EM wave is propagating with an Electric field represented by E = y(hat) [5e^(-jkx)] V/M.

In which Cartesian direction is this EM wave traveling?

I know the answer is +x direction..

However, I'm curious as to why this is. In a sourceless region, there would be no current, correct? Because there is no charge, therefore no current, and therefore no magnetic field?

Correct me if I'm wrong, but a charge has to be in motion for an electric field to produce a magnetic field, right?

So if there's no charge, and no B-field due to a static E - field.. how does an Electromagnetic wave exist, and how does it travel in the +X direction?

From my understanding, an EM wave is produced by succession of induced electric and magnetic fields.

Any help would be great!

 

Correct me if I'm wrong, but a charge has to be in motion for an electric field to produce a magnetic field, right?

The electric field has to be changing, either because it is moving or because it is waxing and waning as in an EM wave.

Yes the lack of sources or sinks is an idealisation that allows the equations to be set up and solved.

Why is this a homework question, it doesn't really seem to fit this section of the forum?

 

My apologies. It was a homework question.. I just wanted to know why the answer was in the +x direction. I knew the answer because it was in the back of the book.

 

My apologies. It was a homework question.. I just wanted to know why the answer was in the +x direction. I knew the answer because it was in the back of the book.

It's because you are looking for solutions to the equations with harmonic time dependence - there is an implied factor of exp(jωt) in the solution.

If you put this in, your solution is a constant times exp(j(ωt-kx))

Any function of the form f(ωt-kx) is called a wave function. You should look this up and try to understand why this is so and why it is propagating in the +x direction.

You do need moving charges to set up EM fields, but these fields can (and do) propagate through source free regions, and here they satisfy the source free equations - that can be separated into the wave equations. This is just a useful technique - it doesn't allow you to work out the fields without knowing anything about the sources, but it does allow you to say some things about them - for example that the propagate at the velocity of light.