E&M - Electric Field Intensity in Microwave

[AngelofMusic]

Hi,

This problem has me stumped and I keep thinking that I'm missing something simple. The question gives us a simple model for modelling a microwave. We consider a plane wave traveling through an object in the microwave (in the z direction), with no reflection.

So, the general form should be; $$E(z) = E_0e^{-yz}$$

We are given that the waves radiate 500W of power at f = 2 GHz in a cylindrical volume with radius r=4. The object has an outer layer 5mm thick. We are also given $$\epsilon_r$$ and $$\mu_r$$. And we have to find the peak electric field intensity at the top of the surface.

Any ideas where to start on this one? I assume it's asking for E0, but I don't know what theorems I should apply to get that one. Maxwell's equations only give me the general solution I posted above. I tried doing boundary conditions, but that didn't get me anywhere either. I have a feeling it may have something to do with the power and the frequency, and possibly the Poynting Theorem. And maybe I should integrate $$P = 1/2 \int |E|^2 dV$$ over the cylindrical volume and set P = 500 W?

Am I on the right track? Thanks for any help you can offer!

 

[Almsco]

Yes, it sounds like you are on the right track. You can use the Poynting theorem to calculate the power density, and then set it equal to 500 W over the cylindrical volume. This should give you an equation for E0. From there, you can use the general solution you posted above, E(z) = E_0e^{-yz}, to find the peak electric field intensity at the top of the surface.