# Speed of EM waves in material

1. Mar 31, 2014

### FaraDazed

1. The problem statement, all variables and given/known data
An EM wave with frequency 87Mhz travels in an insulating ferromagnetic material with $\mu_0 \mu_r = 1000$ and $\epsilon_0 \epsilon_r = 10$ - What is the speed of the EM wave in the material.

2. Relevant equations
$v=(\sqrt{\mu_0 \mu_r \epsilon_0 \epsilon_r})^{-1}$

3. The attempt at a solution

For part A I am really confused, well kind of, I am wondering whether in the text for part A they made a mistake and it should be just mu_r=1000 and just epsilon_r=10 , instead of the product of them and the constants sub0. Because if I do it as in the question I get a speed of 0.01m/s as shown below.

$v=\frac{1}{\sqrt{10 \times 1000}} = 0.01 m/s$

But if I take it to be the relative values on their own I get a much higher value as shown below.

$v=\frac{1}{\sqrt{8.85\times 10^{-12} \times 1000 \times 4 \times \pi \times 10^{-7} \times 10 }} = 2.99 \times 10^6 m/s$

So my question really, is it possible to have such slow propagating EM waves in materials like that?

2. Mar 31, 2014

### Simon Bridge

I think your intuition is good - ferrites typically have speeds of order 10^6m/s.
You can look up typical values or permitivity and permiability for various ferrites online and compare.

The trouble is, you cannot rule out that the material here is fiction for the purpose of teaching/testing you.
You should ask someone.

note: relative permiability is sometimes written as $\mu/\mu_0$ which could be a source of a typo.

3. Apr 1, 2014

### FaraDazed

Thanks. I emailed the lecturer on the basis of your reply and yeah, it was a mistake.

I get what you mean regarding it could have been a possible make believe scenario (thats why I wanted a second opinion) as they are prone to doing that. The other day on another modules homework we had to workout the de Broglie wavelength of an Ewok running on Endor where the 'h' has a value of 1000 Js! . (Sorry to detract from the OP) but knowing he would have a relatively large wavelength, what would the implications of that be, i.e. him running. Would he simply madly "interfere" with himself?

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