Hi Sai Krishna Garlapati ,

an EM wave has no constant components. So the source of the constant B component has to be something different, like a permanent magnet.

Just as a thought experiment, if you had parallel planes made of a non-ferromagnetic material which can be somehow switched between PEC state and non-PEC state, then you could switch it to non-PEC, attach a permanent magnet on the outside, and switch it back to PEC. As a result, you'll have a constant normal B component, both on the outside and on the inside of the waveguide, and the parallel planes could guide EM waves as before.

However, if you approach a (non-switchable) PEC plane by the source of a constant magnetic field, the changing external field will cause eddy currents in the PEC which in turn will keep the B field on the inside of the PEC at zero. As a result, even if you succeed in forcing a permanent magnet to touch the surface of the PEC, there would be only tangential B components at the surface.

Dear Sai Krishna Garlapati,

Please look for the details of your interesting inquiry at chapter IV, pp. 107 in Electrodynamics of Continuous Media: Volume 8 by L. Landau and E. Lifshitz, Pergamon press.

There can only be a tangential component of the magnetic field if it was there at the beginning of the universe, or when the conductor became perfect. If the magnetic field started later, then as it grew, it would induce currents in the perfect conductor that would exclude the magnetic field. Because it is a perfect conductor these currents never die out by themselves, so continue to exclude the magnetic field for ever. These currents have the effect that, inside a perfect conductor, there is a virtual image of the magnetic field outside. The parallel component is in the same direction, but the normal component is in the opposite direction. The normal components cancel at the boundary.

For non-perfect conductors the effects are similar for timescales in which the currents don't die out much in a half cycle, and over distances larger than the skin depth. In a perfect conductor the surface current has infinite density and zero thickness.

One difference between superconductors and perfect conductors is that when a superconductor forms, it will exclude magnetic fields that already exist inside it, whereas a perfect conductor would not. Another difference is that superconductors exist but perfect conductors don't!

Very interesting, Dear Prof. Malcolm White. Thank you. I guess this could be the attenuation of persistent currents in the superconductor. Persistent current is bound current, not having any charge accumulation associated with it, since it is divergenceless [1].

[1] https://en.wikipedia.org/wiki/Persistent_current

There is no attenuation of persistent currents in a superconductor.

Also, a superconductor is not the same as a perfect electrical conductor (PEC). They behave differently.

Adding to the colleagues,

If the tangential electric field is zero for perfect conductor, then the tangential current is zero. Since the magnetic field resulting form the current flow is in a normal plane to this current, then the normal magnetic field will be zero.

This may be an answer of your question.

Best wishes

Abdelhalim abdelnaby Zekry For a perfect conductor, there can be a large current tangential to (along) the surface, for zero electric field. Resisitance(=0) = voltage(=0)/current(can be anything).

The tangential magnetic field is normal to the current direction, and is equal to the surface current density in Amperes per metre.

Thank you Malcolm White . I assumed that the current can be anything equal to zero. and so the magnetic field in the plane normal to the current flow will be zero as Integral H.dl=I=0.

Best wishes

Abdelhalim abdelnaby Zekry I think I don't understood your reply. The surface current can have any value, it can be zero, but only if the tangential magnetic field is the same inside and outside the perfect conductor. The only way that there can be magnetic field inside a perfect conductor is if it was there before the material became a perfect conductor. As there are no perfect electrical conductors the question of how this could happen is meaningless. If, starting from no magnetic field, a magnetic field is applied to a perfect electrical conductor then eddy currents will start in the conductor that will exclude all the magnetic fields from the perfect conductor, and won't stop because they are lossless. There are no voltages associated with these persisting currents, except those due to Faraday's law, when the fields were changing. As there can be no magnetic fields inside the conductor, the normal component of the magnetic field must be zero, as it cannot stop dead at the surface (as it can on a permanent magnet). The tangential component of the magnetic field can exist outside the perfect conductor, but not inside, so the discontinuity is equal to the tangential field strength, so the surface current density has to be equal to the magnetic field strength. Because it is a non-physical perfect electrical conductor you end up with infinite current on a zero thickness layer.

Superconductors are a bit like this, but with the difference that when a (simple) superconductor becomes superconducting it excludes the magnetic field from itself, except for a thin skin around the outside, and the surface currents extend through this thin skin depth so there are no infinities.