Question

How does the construction of the Van de Graaf demonstrate these two scenarios?

1. The electric field strength near a charged conductor is greatest in the vicinity of the most sharply curved surface therefore air is likely to ionize and initiate a spark near sharp points.

2. it can be shown that if coulomb's law is correct all the static electrical charge on a conductor must reside on its outer surface

Answer 1

Let us consider two conducting spheres as shown above connected to each other by a conductiong wire.

The potential of sphere 1 is

The potential of sphere 2 is

As the two spheres are connected by a wire there potential must be same

where is the surface charge density

Therefore lesser is the radius more is the charge density. At sharp ends, the radius is very less so the charge density at these points is very high so the electric field in the vicinity increases.

b) In a conductor If a charge is put inside the conductor surface then due to coulomb's repulsion force they will repel each other and since conductor allows them to move under this repulsive force the charges tend to move away from each other and reach to the maximum extent. This way all the charges come on the outer surface of the conductor.