Question: Why is an antenna is used in this electronic [electroscope circuit](http://amasci.com/emotor/chargdet.html)?
I would like to do this as my mini project.

Answer: 
The antenna is used to pick up an electric field (*not* the same thing as a radio signal). It can be any length but I'd expect that the further away from the ground plane of the circuit the "stronger" a field you will get.

The "optional" 1Mohm resistor is really ought to be included otherwise you risk damaging the FET through electrostatic discharge.
it's not really an antenna in the normal sense .... it's a metal so it's a sea of electrons, when there's an electric field around they all get attracted down one end leaving the other end with the opposite charge, since it's connected to the gate of the FET the FET turns on or off, depending on the charge

As mentioned above a 1M resistor on the gate would probably be a good idea