# EM waves

1. Feb 7, 2009

### noppawit

Show that the electric field: E = Emsin(kx-ωt) and magnetic field: B=Bmsin(kx-ωt) satisfy the following equations:

$$-\frac{\partial B}{\partial x} = \mu_{0}\epsilon_{0}\frac{\partial E}{\partial t}$$

and

$$\frac{\partial E}{\partial x} = -\frac{\partial B}{\partial t}$$

Thanks.

Last edited: Feb 7, 2009
2. Feb 7, 2009

3. Feb 7, 2009

### noppawit

Sorry for my bad Latex typing.

I've edited.

4. Feb 8, 2009

### AEM

In a situation like this, the usual procedure is to substitute the two given expressions into the differential equation, take the derivatives and see what happens. As I look at what you've been given (without working it out myself) I think you may have to figure out how to relate $$\mu_o \epsilon_o$$ to k and $$\omega$$.
That should get you started. Let us know if you run into trouble.

5. Feb 8, 2009

### AEM

Upon reading my previous post, I see a small problem with what I wrote. When you substitute the expressions for E an B into each equation, you'll end up with a $$B_m$$ on one side and a $$E_m$$ on the other. That's a nuisance. However, I'll bet you can figure out a way to combine those two equations into one equation and then do the substitution.

6. Feb 8, 2009