Final answer:
The pith ball does not move through the electroscope to Earth because the electroscope is not directly connected to Earth. If the electroscope were grounded, excess charges would flow to or from Earth, neutralizing the electroscope. Charging by induction is another method that polarizes a neutral metal sphere by a charged rod and grounding it.
Step-by-step explanation:
The reason the charges don't simply move through the electroscope, through the bench, and to Earth is because the electroscope is not directly connected to Earth. When the pith ball is charged, excess charges are distributed throughout the electroscope, causing its leaves to separate. However, since the electroscope is insulated and not grounded, the charges cannot easily flow through the bench to Earth.
If the electroscope were grounded, meaning it had a conducting path to Earth, the excess charges would flow from the pith ball through the electroscope and to Earth, causing the electroscope to become neutral again. In this case, the leaves of the electroscope would come back together.
Charging by induction is another method where a neutral metal sphere is polarized when a charged rod is brought near it. The sphere is then grounded, allowing excess charge to flow to or from Earth, resulting in the sphere having an opposite charge to that of the rod.