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Yes, the guitarist can create a hum but usually when you touch the strings the opposite happens.
Your computer is not really running from the mains, it's charging and powering the battery. I would never have said your computer has no earth potential, even if the power supply has no earth the case is connected to earth. So all the time you only have one source of earth there is no hum, introduce another different source of earth and it creates a hum.
I'm not going to try and give you a definitive answer to why without having a close look at the equipment involved and running some tests but the problem is the potential difference between 2 pieces of equipment and it's a nightmare in sound engineering because different designers have different approaches.
Almost all systems have some noise, it's a question of how much gain you apply to it. Guitars/Mic Inputs/Phono Stages are all small amplifiers providing a lot of gain so they are a common source of noise.
Just to say I've built phono amps, amps and all kinds of micro electronics but don't pretend to understand them in any great depth. I'm also a qualified electrician but when I have the same problem as you I leave the thing plugged into the usb port.
Airhead-
yeah, ground hum is an absolute pain in the arse. I'm an electrical design engineer - for consumer products we build to standards to pass safety certification so as long as you're within certain tolerances it's 'fine'. For things like audio equipment, however, fine for a safety standard doesn't necessarily cut it for audio quality / interoperability.
This is why I suggested lifting the ground on a power supply connecting to the 5v usb port. It's a low voltage circuit which has already been identified as being able to fix the problem. Saves the hours of ground hum problem solving you'd have to do plus it's not risking any safety problems.
gorgonzolach
If that was the case removing the computer from the outlet and running it on battery would sort the problem?
On a guitar I guess even the person holding it can work as a 'ground loop'? specially if bare foot... :D