Why We Don’t Use Wood As the Core for Transformers?

The core of a transformer does not have to have “magnetic properties”. Air doesn’t have magnetic properties (well, ok, oxygen is slightly paramagnetic, but that’s small enough that we can ignore it in most practical applications), and yet we use air core transformers all the time.

The reason we don’t use air core transformers for high-power, low frequency transformers (such as those used in power distribution systems) is because air core transformers have much lower inductance than a comparable transformer wound on a core with significantly more permeability than air. A transformer with the inductance desired for most power applications would be absolutely huge without using some sort of high-permeability core. However, for low-power, low-impedance inductors and transformers, an air core is perfectly acceptable, often even desirable. The behavior of air-core transformers is easier to predict, because you don’t have to deal with the nonlinear behavior that iron-core transformers have. The permeability of iron, indeed all magnetic materials, varies with flux density; a non-magnetic core avoids this issue.