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Characteristic impedance (Z0) is defined as E/H ratio of {E,H} field.

It depends on dielectric permettivity (epsilon), magnetic permettivity (mu) and geometry of region in which {E,H} propagates.

For free space, it's easy to believe that geometry coefficient is 1 and in the end, you get

-> Z0= square root (mu 0 / epsilon 0) = 120 pi,

where subscript 0 means mu and epsilon referred to free space and pi=3.14...

If you want to demonstrate that, you have to solve Maxwell's equation, imposing the condition of uniform plane wave travelling into free space, so you'll get an Helmholtz equation for Coulomb electric potential phi (you have to apply Lorentz's gauge condition and you'll get laplacian(phi) + k^2 phi = 0, where k=2*pi*frequency/c0 is called wave number). You solve this equation and put it into the equation linking magnetic potential vector (A) and phi. At this point, you can solve Maxwell equations and get E,H values and modulus ratio (Z0).

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Q: What is the characteristic impedance of free space and why do you think so?
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