Need help finding cause of hum

I'd appreciate input on something I just noticed. The right channel of my system is producing a very soft, low level (low db) hum right on power up and with the volume all the way down. It's only noticeable with your ear an inch from the midrange/bass driver. It doesn't change level if the volume is increased. It is not audible when playing music. It has done this with 2 different amps (1 brand new). It does this whether or not input sources are connected. It does this whether the ground between TT and phono-pre is connected or not. When I switched the left speaker/cable to the right amp output and right speaker/cable to the left output - the hum moved to the left. So I thought, hmmm, problem with amp. But it is now doing this with a brand new amp. When I reversed speaker placement (Right to Left & Left to Right) - cables staying in place - the hum stayed on the right coming out of what had been the left channel speaker. The hum is only heard on the right. The left is totally silent. I usually run the amp plugged into one wall outlet and other gear out of an APC H10 power conditioner plugged into a different outlet on that wall. I tried plugging the amp into the amp power outlet on the back of the APC but the hum remained. I tried plugging both pieces (H10 & amp) into the same wall outlet. The hum remained. I thought this might be some type of ground loop hum but from what I've read, it doesn't seem consistent. It is only out of the right channel and barely audible. It is more a curiosity than annoyance at this point but I am concerned about the possibility of some sort of induced, stray current causing damage. Any ideas you might provide will be very much appreciated.