Q: “How does balanced power help to solve ground loop humming?”
A: Using balanced power can help solve certain ground loop problems because it takes its ground from one source, thus having no potential difference. You can do this yourself simply by taking all your power from one outlet or circuit. If your equipment “leaks” to the ground, meaning current is flowing to the ground wire, then balanced power might be helpful. Some people believe that balanced power solves all ground loop problems, which is not the case. It is still possible to create ground loops with balanced power. There are, however other problems that can be solved or improved by using balanced power.
In theory balanced power solves certain problems in a manner similar to how a balanced audio signal does, especially noise cancellation. The typical claim made by manufacturers of balanced power equipment is: “When the power is balanced the main power cable has less electromagnetic field around it, so it should induce less noise to nearby audio cables”. Those claims are partially true. If you placed an unshielded cable next to a balanced power cable, quite a bit less noise/hum would be picked up. If you placed a shielded cable next to a balanced power cable less difference would result. The capacitively coupled portion of the signal is intercepted nearly completely by the shield. Much of the inductively coupled component will reach the screened signal wire(s). Magnetic field around the cable will be practically the same whether the power cable is balanced or not, as there is still the same amount of current flowing up one wire & back down the other.