How is a conducting object charged when it touches a van der graaff generator? Does it have the same charge as the generator?
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The Van De Graaff generator would have some unequal charge distribution, Q. For convention's sake, let's assume that it has a net negative charge.
When a conducting object (which is neutrally charged) is touched to the Van De Graaff generator, the negative charge attempts to discharge to the conducting object as to equally distribute the charge.
Then, once the object is taken away from the generator, the charge is still held on the conducting object.
Think of it like this. Let's assume that there are n "extra" electrons swimming around the Van De Graaff generator, causing some net charge of -n. Since electrons repel eachother, they will jump to any surface possible to try to get as far as possible from eachother.