# EM: Transformer confusion

1. Jan 26, 2008

### Very curious

I understand that according to Maxwell's equations time-varying EM fields cannot exist in a perfect conductor (but static magnetic fields can). Also if you have a time-varying magnetic field you also have time-varying electric field and vice versa. And this knowledge is used to solve EM wave problems by fixing boundary conditions between conductor and dielectric mediums.

However, I get confused/baffled when I try to apply this boundary condition (that time-varying EM fields cannot exist in a conductor) to a transformer with iron core. I understand that a changing current creates a changing magnetic field (by Ampere's law?), which I assume is equivalent to a time-varying magnetic field, in the iron core.

Now, since the core is a good conductor shouldn't there be no EM field within it? But then, this would imply no time-varying flux within the iron core and transformer cannot work, which is obviously not true. Could someone kindly help me reconcile these two examples? Where did I go wrong? Thanks in advance.

2. Jan 27, 2008

### pam

In iron, the magnetic field falls off rapidly with penetration so that
$$|B|=\mu H_0 \exp[-z/2\delta]$$, where
$$\delta=c/\sqrt{8\pi\mu\sigma\omega}$$ (in gaussian units) is the
"skin depth". An integral of this B gives the flux.

Last edited: Jan 27, 2008
3. Jan 28, 2008

### Very curious

Pam, thank you. Your answer may explain why the transformers are made of laminated iron cores. I just assumed the lamination was to reduce eddy currents but I guess it also is a way to get around skin effect of single core to carry more flux. One more thing, within the skin depth, the time varying E field exists also, right? I guess making transformers with superconductor cores may not be a good idea.

4. Jan 28, 2008

### TVP45

Pam,
You make a good point about the problem with iron. Because of this, most transformer and motor laminations are made of silicon steel (often grain oriented), or cobalt alloys, or nickel alloys which, among other benefits, significantly raise the resistivity of the metal.