Multimeter reading between wire & air Why does a multimeter show 10-20 V(AC) when I connect one of its cables to the hot wire of a 220 V(AC) plug while the other cable is in the air? Also why does this not happen with a 5 V battery? (It just shows 0 V)
 A: The capacitance of your multimeter to Earth completes the circuit. You don't measure the full voltage because the impedance of the meter's stray capacitance to Earth and the meter's finite input impedance make a voltage divider. Even this very small capacitance permits enough current to pull the potential of the disconnected lead of the multimeter away from the potential of the other lead, and thus there is some (small) voltage across the multimeter.
There's a much more visible, and awesome demonstration of this mechanism. Have you ever seen how high-voltage lines are serviced by helicopter?

They don't turn them off for routine inspection and maintenance. They fly up in a helicopter, and someone climbs on them. Even though the helicopter isn't touching anything else, the capacitance of the helicopter to the other wires and Earth is significant enough that a pretty substantial current can still flow. As the lineman approaches the lines, and as the helicopter is flying away, he holds a probe out that shoots sparks for many feet. Better to have them shooting out the probe than your eyes. The lineman is also wearing a conductive jacket so all that current flows through the jacket and not the lineman.
Of course this line is at 500,000V, which makes things a bit more spectacular than the 220V in your home. The voltages involved on these lines is sufficient to ionize the air and that's why you get these great sparks: with just 220V you don't get lighting bolts, but there are still invisible displacement currents.
It doesn't work with a battery because a battery is DC, and any capacitance is an infinite impedance at DC. Because there's an infinite impedance between the disconnected lead of the multimeter and the disconnected end of the battery, the disconnected lead of the multimeter will (at equilibrium) be at the same voltage as the connected lead, and thus, no voltage across the multimeter.
See also Why one of my multimeter shows a small voltage when only one probe is connected to AC and the other dont? on electronics.SE.
