$2.(10$ pts$)$ A Van de Graaff generator is an electrostatic device that uses a moving nonconductive belt to carry electric charge into a hollow metal sphere. This sphere is insulated from the ground and can accumulate charge until enormous voltages are reached. Small Van de Graaff generators are exciting novelties while large ones are used in research and industry.

a$.(3$ pts$)$ A typical Van de Graaff generator uses a rubber belt to carry negatively charged electrons from its base to the sphere. As the belt passes through the sphere, a metal brush touches it$.$ Electrons leave the belt and flow through a wire to the surrounding sphere. Why do they flow onto the outside of the sphere rather than staying near the belt?

b$.(2$ pts$)$ The amount of $($negative$)$ charge that can build up on the sphere depends on the size of the sphere$$s surface. Why is it important that there be no sharp points on the sphere?

c$.(3$ pts$)$ As you move your hand close to the negatively charged sphere, your hand becomes positively charged and a spark may leap from the sphere to your hand. Why does your hand acquire a positive charge, and from where does it come?

d$.(2$ pts$)$ If you insulate yourself from the ground and put your hand on the sphere, negative charge will accumulate on you as well as on the sphere. Explain why your hair stands up$.$