# Impedance of free space/wave impedance

1. Apr 15, 2010

### fluidistic

If I'm not wrong, empty space (vacuum) has the greatest impedance amongst any material. Because $$\eta = \frac{1}{n} \sqrt {\frac{\mu _0}{\epsilon}}$$ if I'm not wrong and n=1 (smallest value possible) for free space. What does this mean that free space has a big impedance? It makes the greatest opposition to electromagnetic waves? I'm not getting the meaning of impedance in this case.
P.S.: I've searched in wikipedia, also wave impedance but didn't find any explanation about the meaning of it.

2. Apr 15, 2010

### Antiphon

It is not always true. In a material with high mu but not very high epsilon, the impedance would be much higher.

Don't think of it as opposition, that's not correct. Think of it like this: the natural ratio of electric to magnetic fields for waves in that medium is the impedance. It's not a statement about the difficulty of the waves travels.

3. Apr 15, 2010

### fluidistic

Ok I trust you, although I've some doubt since n would/could be big in those materials? I'd appreciate if you have the name of at least 1 material whose impedance is greater than free space; if you don't, no need to lose your time searching this for me, I'll trust you anyway.
Ah ok, so I should only look at the mathematical definition. I wonder why they called this "impedance".

4. Apr 15, 2010

### Antiphon

Impedance is a close cousin to resistance. The names are motivated by the same concepts but impedance is a frequency domain quantity and is complex (R+iX) where the real part is the resistance.

5. Apr 15, 2010

### fluidistic

Ok so there's definitely a relation with the electrical impedance (which I was aware of). It's not obvious to me from the definition of the free space impedance.

6. Apr 15, 2010

### Antiphon

It is the same concept (and units) except for the definition. In a circuit it's the ratio of V to I at a point in a circuit. In the full field problem it's the ratio of certain components of the E and H fields.

A ferrite is an insulating material where mu can be hundreds of times greater than epsilon. These are used as cores in high frequency coils in circuits.

7. Apr 15, 2010

### fluidistic

Thanks once again for this reply.
Does it has any sense to talk about a refractive index in ferrite? I know light gets absorbed (and thus refracted?)/mostly reflected in metals. Although ferrite is a composed material, I think that some light can pass through the ferrite a small distance.
Anyway the refractive index appears in the definition of the impedance (in my class notes, but I didn't find it in wikipedia), hence my question.

8. Apr 15, 2010

### SpectraCat

Refractive index is also a complex quantity:

$$\tilde{n}=n + ik$$

where n is the real part of the refractive index (the "normal" one that we use e.g. in Snell's law), and k is the extinction coefficient, which becomes important when the material is absorbing radiation. This can be resonant absorption, as in a dielectric, or conduction band absorption, as in a semi-conducting or conducting material.

So yes, ferrite has an index of refraction, but the complex index is large, because it is absorbing. With regards to the wave impedance expression, I am fairly sure it is only the real part of the index of refraction that enters in, since that expression is for perfect dielectrics (so it would make sense to apply it to ferrite anyway).

9. Apr 15, 2010

### Antiphon

It is best defined in terms of complex epsilon and mu. The index of refraction is an incomplete description of a medium.

10. Apr 16, 2010

### fluidistic

Ok thanks to both, I get it. Very interesting.