An initially neutral rubber rod is rubbed with fur, so that the fur becomes positive. The rod then briefly touches an uncharged electroscope and the leaves of the electroscope separate and stay separated even after the rod is removed. Finally, a second rod with an unknown charge comes near the electroscope without touching it and the leaves of the electroscope move farther apart. What is the charge of the second rod?
The rubber rod is neutral and when rubbed with fur the fur becomes positively charged. As total charge must remain constant, the rubber rod must have acquired a negative charge.
It is then touched with an electroscope which hence becomes negatively charged because the rod transfer negative charge to the electroscope and they remain separated as like charges repel.
The unknown rod increases the separation without touching it. This means the magnitude negative of charge must have increased after the unknown rod is held at a distance. This is only possible if the unknown rod induced a negative charge, which is only possible if the rod itself is positively charged. So the unknown rod is positively charged.
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