Toroidal transformer orientation

[shakalnokturn]

This is an already solved problem, I'm curious to hear if other people have run into this before and the explanation behind it.

I had a AER guitar amp to repair with a defective toroidal power transformer. 60VA, 2x115V series primary, 2x15V parallel secondary.
The transformer supplies an internal AGM battery and inverter for the power amplifier supply voltage. It's mounted under the charge / inverter PCB and furthest away from the high gain stages.

I thought the replacement would be straightforward, it was a tight fit, the replacement being slightly more powerful and bulkier than the original (not larger enough for distance to have significant effect on radiated fields). Once replaced there was some 50Hz hum. The owner confirmed this was not the case before the transformer replacement so I went back and re-checked wire routing.

In the end the hum was eliminated by rotating the transformer around it's mounting axis by 90° having the wires rather counter-intuitiveley right against the inverter PCB.

[Jwillis]

In theory the field should be confined just to the core as the outer field plain should cancel the inner field plain. But the math is based on ideal conditions and as we all know reality isn't always ideal. Some stray magnetic flux will escape because the outer winding's are not evenly spaced with the inner winding's. But if you look at the toroid in 3 dimensions, the top and bottom winding's are evenly space with respect to each other. So much better  cancellation of the fields can be achieved on the top and bottom plains. Defects in the core contribute as well to how much the fileld will stray from the centre of the core. The size of the core and number of winding's also effects the amount leakage. This phenomenon is also applicable to toroid chokes. By placing multiple toriods with the tops and bottoms parallel to each other, neither field will effect the next as much as when the toroids are placed with the outer perimeters side by side.  This effect can be observed with an AC Gauss meter.