I sometimes need air core transformers for contactless energy transfer of small powers (usually less then 1 watt). However, on rotating machines, sometimes a bearing is needed in proximity of the energy transformer. The bearing than gets some coupling to the transformers field and as it's steel just forms a shorted winding, consumes some energy.
Now I have the case of a larger bearing, spanning about half of the transformer coils plane. Obviously, it will short out much of the energy transmitted.
I wonder if it would be possible to remove the inner part of the field, by adding some reversed windings of the bearing diameter to the primary coil. The primary field would then be constricted to the outer part of the primaries core area I guess, leaving the bearing uncoupled. But how many windings would that take? The same amount as there are forward windings in the outer coil?
The situation is most likely this: red: coils, grey: interfering metal, non-metal parts omitted.