Question about the Earth acting as a conductor/ground

[NeuronalMan]

Homework Statement

Hello, I'm a little confused about the statements regarding conductors grounded to large conductors, as the Earth. Basically, my physics textbook says that metal sphere with a positive charge and ground it to the Earth, electrons from the ground will neutralize the positive charge. That's understood. But is this to say that the Earth, or any large conductors can only neutralize positive charge? If a building is struck by lightning and there's a lightning rod on the top of the building, doesn't the lightning rod conduct the enormous charge to the Earth, which is the opposite of my first example? So I can't seem make this concept disambiguous, as I thought that an entity could only have one of the two features. I am having the same conceptual problem with the Van de Graaf generator. There's a girl touching the dome, subject to electric potential, while standing on a platform insulating her from the floor. So she's not grounded. If she was grounded to the Earth, would it be the Van de Graaf generator conducting the charge to the Earth, or the Earth neutralizing the girl?

I know this is very basic, yet it's not altogether clear to me. So an answer is deeply appreciated.

Homework Equations

The Attempt at a Solution

 

[Chi Meson]

What you need to "get" is that it is not the quantity of charge that is important, but the voltage (electric potential). A useful way of thinking of potential is consider it like the density of net charge. That is not quite what it is, but go with it for now.

The Earth is very large, and if it gives up a few electrons to neutralize a positive charge on a relatively tiny positive sphere, that tiny quantity of charge will not change the potential (voltage) of the earth. Divide that charge over the entire surface of the earth, and you will still have a neutral earth.

The Earth has the ability to give or take enough electrons to neutralize any positive or negative net charge.