Recently I was toying with a digital multimeter and observed the following. The multimeter was set to measuring AC voltage with the upper limit of 750 volts. It has two probes which I will call "red" and "black" to better illustrate what happened. Both probes were connected to the multimeter and I didn't alter their connection to the multimeter.
I inserted both probes into mains (220 volts in my region) outlet - one probe per outlet hole - and it showed something around 220 volts. Now I unplugged the "red" probe from the outlet while leaving the "black" probe plugged into the outlet - the multimeter displayed zero. I plugged the "black" probe back into the outlet and unplugged the "red" probe from the outlet - the multimeter displayed about 7 volts.
So again, one probe was connected to the multimeter and the outlet terminal and the other was only connected to the multimeter with one end and the other end of the second probe was pointing in the air - not in contact with anything. The multimeter displayed 7 volts.
Why did the multimeter behave that way? Where do those 7 volts come from?
Answer
The same thing is going on as when you touch the end of a audio cable going into a power amp and power line hum comes out of the speaker. Your body is like the multimeter probe that is not connected to anything. Since there are power lines in the vicinity, your body picks up a little bit of that AC signal capacitively, and that gets coupled into the audio cable which the amplifier then amplifies to drive the speaker.
Multimeter inputs are high impedance deliberately so as to minimize how much the meter effects what it is trying to measure. Let's say the meter impedance is 10 MΩ. How much capacitance in series with 220 V at 50 Hz would it take to have it see 7 V? The capacitor would have to have about 3 GΩ impedance, which takes about 1 pF at 50 Hz. 1 pF is plausible enough for coupling from the loose meter lead back to the power line.
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