A Fundamental Electromagnetics Question

Lets say you have both epsilon and mu (permiability and permittivity) equal to 0. Does this mean that the Maxwell equations reduces to static equations. What do you think?

Hi,

Epsilon and mu can never be 0 (they are constants), even if you have a non-magnetic material the relative mu_r is equal to 1. Another reason why epsilon and mu cannot be zero is that when solving the wave equation (for simplicity assuming charge free and current density free medium) the propagation constant (c, i.e. the speed of light would be infinity which violates so many things it's not worth listing here) is composed of epsilon and mu.

If you want the static equations set all time derivatives to zero, this will allow for the decoupling of the electric and magnetic field.

-Jayson

Zo=sqrt(μo/έo)
If you say both/or one of them are 0 , what would be characteristic impedance?

You are right in a sense because these units are derived with one thing in mind that c velocity of light is 300Km/sek from Einstein theory.

But for now just stick to what we have.

well, if both epsilon and mu are analytic functions of frequency and if they can both be negative (It has been shown that both can be negative at the same time), then at some frequency point shouldnt we have at least one of them equal to 0? Still the speed of light is not affected. These are just the relative epsilon and relative mu. But if you start from the Maxwell equations and put epsilon and mu equal to 0 after you derive the wave equation all the equations reduces to the static equations.

I think we need to look at the fundamental constituitive relations that is the ones that relate ( E and D ) and (H and B) .Let us consider only E for the time being.D=eps0E+P where P is the polarization vector.Now if we say that Epsr=0 what happens is that in response to any excitation ( I mean external electric field ) the material generates an equal and opposite polarization inside it and hence in the substance , D and hence charge density and hence the net field would be zero . This hold for magnetic fields too.Hence I feel that having both Epsr and Mur zero would amount to zero fields in the material ( not just that the time derivates of field are zero as required by statics but the fields themselvers would be zero).The argument is based on "if epsr and mur are zero" but how epsr and mur are made zero , I do not know.

Please point out any fallacies in my arguments.

I think ifan1 talkd about that epsilon and mu were equal to zero simultaneously based on the dispersion formula,if just considering from matemateics, it looks possible.But from physical view, it's hard to explain at least the classic physics cannot solve it now. But those dispersion definition for epsilon and mu are produced based on classic physics.

I think irfan1 is talking about metamaterials, materials which are characterised by negative permeability and permittivity at some frequencies. He correctly points out that these materials have negative epsilon and mu at some frequencies and positive eps and mu at others (this is not a mathematical exercise, it has been measured experimentally in some artificially created materials).

obviously there is a pass through zero, and his question is what is happening at that frequency. I'm not an expert on this, but my feeling is that there is no propagation of EM waves provided the propagation constant vanishes.

How can U have both zero?? I couldn't understand. The material should be either magnetic or eletric. It cannot be neither. Is there some material that exist with εr and μr as zeros??

If you have a material with epsilon = 0 and you use it as a capacitor dielectric, then the capacitance is zero. Likewise with mu = 0 and an inductor. That would be a scary universe!

For me, most of the arguments made are true in their own context. Yes its true that artifically metamaterial show bothe μ and ε for a cetain range of frequencies. But it is seem impossible to make both of them zero at the same frequencies.

I want to point out one thing. It has been argued that some artificially engineered materials show positive permittivity and positive permeability in one range of frequencies and negative values in an another range. Hence there must be a frequency where the zero crossing occurs so that ε and μ go to zero.

I think we should pay attention to the fact that in real universe, perfect conductors/insulators and magnetics do not occur. Hence even if the real parts of ε and μ go to zero, the loss factor due to imaginary parts of ε and μ always remain. As a result we might be looking at attenuating waves in that regime.

Let me know what all of you feel.

-svarun

Hi svarun:
Yes you r right if we think of unbalaced case of CRLH TL we will find that gamma is purely imaginary which means your argument is true.
have a look on attached file

if both epsilon and mu are simultaneously zero, then there are no propagating waves inside the medium. Which in turn would mean that there would not be any absorption. Lets try to think in terms of macroscopic Maxwell equations. for a particular frequency, at which both epsilon and mu are both zero, the Maxwell equations are just the static electromagnetics equations. but the real question is, would the averaging of microscopic Maxwell equations would permit us to have simultaneous epsilon=0, mu=0?

Hi irfan,

Your question is well founded. If I understand it correctly, you suggest that at a smaller length scale, eps and mu need not be zero but averaging over the entire macroscopic structure, we might be able to get eps=mu=0.

Now, can you clarify what you mean by eps and mu zero ? Does it mean that Re(eps)=Re(mu)=Im(eps)=Im(mu)=0 ? In that case there won't be any waves propagation. But my feeling is that Im(eps) and Im(mu) cannot be made zero even in macroscopic structure at any cost since all losses keep adding. Let me know what you feel.

Regards
svarun

I beleive imaginary parts may be made very small. But I dont yet have a physical reasoning for this statement. But to my experience, whenever eps and mu attain close values, the imaginary parts turn out to be small. Maybe some conclusion based on the linear response theory and Kramers-Kronig relations maybe drawn. On the other hand, since there are no propagating waves when eps and mu are simultaneously zero, the effect of imaginary parts is only some contribution to the scattering or reflection. If in addition, the imaginary parts are close to zero, then you would have two impedance matched mediums. It is a bit difficult to imagine this situation, physically. Waves are coming, they hit a wall, but they are not reflected. On the other hand, they are not propagating inside the wall. More, interestingly, they are not absorbed inside the wall. This is a fascinating phenomenon. I have seen some FDTD simulations, and I did some FDTD simulations myself. This phenomenon really happens. But I have not seen yet a physically sound explanation.

Maybe they transferred to surface waves propagating perpendicular to coming waves.