Arturo O. answered 12/11/17
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The leaves of an electroscope are made of conducting material. Suppose they are neutral at the beginning. When a negatively charged rod contacts the wire that feeds into the leaves, excess electrons from the charged rod migrate down into the leaves, and the leaves acquire a net negative charge. Remember the excess negative charges on the rod want to repel away from each other, but have nowhere to go. Contact with a neutral conductor gives them a path to migrate away from the rod, into the neutral conductor, building up a net negative charge on the conductor.