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I'm talking about when it makes our hair stand up

Let's say the dome is positively charged. I have heard that the van de graff generator is able to remove electrons from our hair.

But isn't our hair neutral? So how does it remove electrons? And also, where do those electrons go?

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Even if the air stayed a perfect insulator your hair would be attracted to a positively charged VdG dome.

The VdG dome produces an electric field which would produce a separation of charges with your hair having a net negative charge and parts of you body and the Earth having a net positive charge.

Because of the repulsion between the strands of hair it would probably also stand on end.

The distribution of the induced negative charges on the hair would not be uniform with the greatest surface charge density being at the most "pointed" parts of the hair - at the ends.
This large surface charge density would produce a large electric field in the air surrounding the hair.

If the electric field is large enough ions and electrons will be produced and hence in effect the air will become a conductor which is called action at points. The electrons will be repelled by the hair and move towards the positively charged VdG thus discharging it and at the same time you are "gaining" positive charge.

The reason for the spherical dome on the VdG is to have an object without any points, edges etc so that the electric field at the surface of the dome is kept to a minimum.
Dust on the dome or dents can reduce its effectiveness in terms of storing charge.

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The positive charge on the dome creates an electric field. The field acts on two components of your hair, repelling positive charges, and attracting negative charges (i.e. your hair, though neutral, can be polarized).

The important thing is, the near-the-dome parts of your hair (which now have excess electrons) may create ions in the air as those electrons both repel their neighboring electrons in the hair and are attracted to air molecules which (because of the electric field) are ALSO polarized (and present a positive end toward the hair, which makes them attractive to negative charge).

Corona discharge or St. Elmo's fire is the name for such field-induced conduction of electricity through air. Yes, it can remove electrons from your hair. The electrons eventually will pull the heavy air molecule to the van de Graaff dome, possibly sticking to other molecules or dust motes as well. Polarization of materials occurs at all sizes, even (Stark effect) single atoms, but the electric field gives more excitation energy to larger-dimension objects.

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