# Homework Help: Velocity of EM waves

1. Nov 7, 2008

### kasse

1. The problem statement, all variables and given/known data

Find the velocity of EM waves as a function of $$\epsilon_{0}$$ and $$\mu_{0}$$

2. The attempt at a solution

$$E = E_{0}cos(kx-\omega t)$$

Using $$v= \frac{\omega}{k}$$

2. Nov 7, 2008

### gabbagabbahey

When you used Maxwell's equations to derive the wave equation, you should have ended up with an answer to this

3. Nov 7, 2008

### kasse

No, I didn't. But I can substitute my expression for E into the wave equation. What is $$\vec{\nabla}^{2}E$$?

$$\frac{\partial^{2}E}{\partial x^{2}} + \frac{\partial^{2}E}{\partial t^{2}}$$?

4. Nov 7, 2008

### gabbagabbahey

Last time I checked, Maxwell's equations were in terms of $\epsilon_0[/tex] and [itex]\mu_0$ not $c$; so you should have ended up with a wave equation where the propagation speed is in terms of $\epsilon_0[/tex] and [itex]\mu_0$...if you didn't, then you did something wrong....I think you should go back to that problem and show me your work.

5. Nov 7, 2008

double

6. Nov 7, 2008

### kasse

Of course...

So $$\vec{\nabla}^{2}E$$ = $$\frac{\partial^{2}E}{\partial x^{2}} + \frac{\partial^{2}E}{\partial y^{2}} + \frac{\partial^{2}E}{\partial z^{2}}$$ (only spatial dimension, not time)?

7. Nov 7, 2008

### gabbagabbahey

Did you even read my last post?

8. Nov 7, 2008

### kasse

Yes.$$\frac{1}{v^{2}} = \mu_{0}\epsilon_{0}$$, so $$\frac{1}{\sqrt{\epsilon_{0}\mu_{0}}} = v$$. That's what you meant, right?

That would mean that (if I substitute my expression for E into the wave equation) $$\vec{\nabla}^{2}E = \frac{\partial^{2}E}{\partial x^{2}} + \frac{\partial^{2}E}{\partial y^{2}} + \frac{\partial^{2}E}{\partial z^{2}}$$.

Can I also write $$\vec{\nabla}^{2}E = \frac{\partial^{2}E}{\partial \vec{r}^{2}}$$?

Last edited: Nov 7, 2008
9. Nov 8, 2008

### gabbagabbahey

Yes.

First, the electric field is vector, not a scalar so this relation is incorrect...second what does this have to do with finding v...or anything else for that matter?