# If free space impedance is real, why is the electric field not attenuated?

Why does vacuum have a nonzero characteristic impedance towards electromagnetic radiation? Intrinsic impedance given by $\eta=\sqrt{j\omega\mu / (\sigma +j \omega \epsilon)}$. It gives slope of transformation of $\mathbf E$ to $\mathbf H$ and vice versa. Here $\eta$ is complex. And in this expression real part is the cause of attenuation and imaginary part is the cause of phase shift.

In case of free space since $\sigma = 0$, we have $\eta = \sqrt{j\omega\mu / j\omega\epsilon} = \sqrt{\mu / \epsilon}$, which is real. This suggests presence of resistive part in intrinsic impedance which means there should be attenuation. Also curiosity is how free space can offer resistance and however, the expression for electric field in plane wave $\mathbf E = E_0 \exp(wt-\beta z)$ where $\beta =2 {\pi}/{\lambda}$ and $\lambda$: wavelength

suggests constant electric field. How can we reconcile the real impedance of space with the expression for electric field, which has no attenuation?

• Welcome to Physics.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. 4) If you get a satisfactory answer, remember to accept it by clicking on the green checkmark. 5) It is not very clear what you are asking; please elaborate. Thanks! Commented Aug 26, 2016 at 22:51
• This question is very poorly presented. Please consider editing to make it clear what you are asking. It should not be necessary to examine links in order to make sense of your question. Commented Aug 27, 2016 at 0:25
• I suppose now this question is clear so you could remove it from HOLD Commented Aug 28, 2016 at 18:00
• How's that, @ACuriousMind? Commented Aug 29, 2016 at 1:53
• I know what you're trying to ask. The post was closed (and I guess downvoted, although that wasn't me) because it's just not written well. You say "the expression for electric field $\mathbf{E} = E_0 \exp(\omega t - \beta z)$ but you don't even define the symbols. For example, what is $\beta$? Also, that expression is not "the expression for electric field", it's just one possible expression, in particular giving a plane wave. These confusions make the question very hard to understand and answer because even though I can tell what you're probably really asking, I can't be 100% sure. Commented Aug 29, 2016 at 18:21

It's important to make the following distinction: it's not that vacuum "has" an intrinsic impedance. It's that electromagnetic waves IN a vacuum have an intrinsic ratio between their electric field (E) and magnetic field (H), which we call impedance. That impedance is given by Z = E/H, and it is a fundamental constant; it's only when EM waves travel through some medium other than a vacuum that the impedance gets altered. The units are Ohms because E is measured in Volts/meter and H is measured in Amperes/meter, and 1 Volt/Ampere is defined as an Ohm. This does not imply that vacuum "resists" electromagnetic waves and dissipates them like a resistor would.

The specific value of Z(in free space) is related to the speed of light, and to the way we define the Volt and the Ampere. You could think of the "impedance" as being what limits the speed of propagation of the wave, if that is helpful.

• This answer makes a common mistake in that it conflates specific units such as Volt, meter, and Amp with the more general notion of dimensions such as electric potential, length, and current. Impedance doesn't have an intrinsic unit. Ohm is just one particular choice. Commented Aug 27, 2016 at 20:17
• I disagree with the statement "it's not that vacuum 'has' an intrinsic impedance". I also disagree with the statement that the vacuum impedance is imaginary. It is not. Similarly to how a transmission line has a real impedance despite the fact that it is non-dissipative, the vacuum has real impedance. Commented Aug 27, 2016 at 20:18
• Okay, you're right about the impedance being real - if it were imaginary it would be either capacitive or inductive. Editing to remove that. Commented Aug 28, 2016 at 22:03
• I stand by the statement that it's not the vacuum that has impedance. To say that it does implies that "nothing" has propcerties, which is nonsense, and which I believe is the source of the OP's confusion. Free space acts LIKE a transmission line with a certain impedance. It is not itself a transmission medium. There is no Ether. Commented Aug 28, 2016 at 22:10
• Note that the energy in an EM wave in a vacuum does not alternate between E and H. There is zero phase shift between E and H. The impedance is real. Commented Aug 29, 2016 at 17:09

The so called free space impedance is a fictitious resistance offered by the free space for electromagnetic radiation. It has a meaning when an EM wave passes through free space. Otherwise you cannot measure such a resistance. But for a material, it has an intrinsic electrical or thermal resistivity and it exists all time. But here, the free space impedance doesn't mean such a resistance. If you look for such a resistance in the absence of an electromagnetic wave you cannot find one. Obviously, it is clear from that equation. The impedance is the property of a medium due to the passage of electromagnetic waves through it.

Now, why the electric field does not attenuate?

The impedance is caused by the passage of an electromagnetic wave. For the passage of an electromagnetic wave through a wave guide, there should not be an electric field component parallel to the conducting boundary of the wave guide. This creates losses as under such a condition a current is generated on the plates. In free space, there is nothing out there to conduct an hence offers no loss.

$$E=cB$$ or
$$\frac{E}{H}=\mu_0 c=\sqrt{\frac{\mu_0}{\epsilon_0}}$$

Permeability is the degree of magnetization that a material obtains in response to an applied magnetic field. Permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. It can also be seen as the resistance encountered on forming an electric field in a medium (Source: Wikipedia).

Hence this resistance exist because there is a speed limit and it is the speed of light in vacuum. One can say that this limit is guaranteed by the permittivity and permeability of the medium. Otherwise vacuum should have offered infinite speed for propagation of electromagnetic waves.

• I agree with your opinion about intrinsic impedance, but in case of a wave travelling in dielectric medium although there are particles to hinder its motion E/H do not attenuate so this cannot be the possible explanation. Commented Aug 30, 2016 at 19:29
• You are not referring to the intrinsic impedance of a dielectric medium. If you prefer that please edit tour question. The intrinsic impedance is a fictitious resistance. It's not actually there, but effects by an EM wave. Then how could EM wave attenuate?
– UKH
Commented Aug 31, 2016 at 13:10
• Yeah thats what i am suggesting that this explanation is not fitting for all cases thus a better explanation is needed Commented Aug 31, 2016 at 15:44