I bought a new PicoScope USB oscilloscope and noticed that when I touch the tip of the probe with my hand I see a 50 Hz signal of 2 volts on the screen. What is causing this? (Or rather, how is the mains 50 Hz sine wave getting through me to the scope?)
There is a small capacitance between you and the power network. Also there is another, different capacitance between scope's ground and power network. Input impedance is high enough, usually 1Mohm, so you create a kind of voltage divider between power network, oscilloscope's probe and it's ground.
This is a purely capacitive phenomenon. Calling it an "antenna" is a bit misleading and is not any better than others slogans.