Why does the Van der Graaf Generator produce a spark?

[raschagas]

Where the electrons come from? Do they leave the sphere or the object? Or maybe even the rubber band inside the generator?

I'm having a hard time figuring this out.

Also, how does this prove the charge of the sphere?

 

[UltrafastPED]

The Van de Graaff generator uses friction to "rub off" electrons, which stick to the belt until they are transferred to the sphere.

The sphere must be very smooth in order for it to build up a significant charge ... sharp points concentrate the electric field, and bleed off the charge.

See http://science.howstuffworks.com/transport/engines-equipment/vdg.htm
and http://hyperphysics.phy-astr.gsu.edu/hbase/electric/vandeg.html

These describe the two main ways to generate the charges; you can test the charge of the sphere by means of Ben Franklin's technique with pith balls ...

 

[raschagas]

I guess get it now. The brush holds the electrons in and gives it away when needed to produce the spark (potential difference.)

Thanks and correct me if I'm wrong.

 

[DrZoidberg]

The brush is there so that the charge can concentrate in its tips and cause a strong enough field to ionize the air.
http://en.wikipedia.org/wiki/Corona_discharge

First the bottom roller becomes charged through the triboelectric effect because the belt moves over it.
http://en.wikipedia.org/wiki/Triboelectric_effect

The charge on the roller in turn induces a charge in the brush which is not touching the belt at all.
http://en.wikipedia.org/wiki/Electric_induction

The air close to the brush then becomes ionized, allowing charge to flow through the air between the brush and the belt. That process charges the belt which then transports the charge to the upper roller where it then flows through the air into the other brush.

Also the faraday ice pail effect plays a key role in allowing the sphere to acquire a very high charge.
http://en.wikipedia.org/wiki/Faraday's_ice_pail_experiment