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A positively charged rod is held near, but not touching, a neutral metal sphere on an insulating…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A positively charged rod is held near, but not touching, a neutral metal sphere on an insulating stand. A finger touches the sphere for a moment. Then the finger is taken away, and after that the rod is taken away. What is the charge on the sphere at the end? Where did the charge come from? What would be the charge if the rod had been taken away before the finger?
Need a reminder? The key ideaShow
Charge is quantised, with C, and it is conserved. A body that gains electrons has a charge . Identical metal spheres that touch share their total charge equally. In charging by induction a body ends with the sign opposite to that of the rod.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The rod comes near. The positive rod attracts the free electrons of the sphere. They gather on the side nearer the rod. The far side is left with a positive charge. The sphere as a whole is still neutral.
Step 2. The finger touches the sphere. The finger joins the sphere to the earth. The rod still attracts electrons, and the earth supplies them. Electrons flow from the earth into the sphere and neutralise the positive charge on the far side. The sphere now has more electrons than protons.
Step 3. The finger goes, then the rod. With the finger gone, the extra electrons cannot leave. When the rod goes, they spread over the whole sphere.
Answer: The sphere is negative, the opposite sign to the rod. The extra electrons came from the earth.
What if the rod had gone first? Then the electrons would spread out again, and some would flow back to the earth through the finger. The sphere would end neutral.
Watch out. The rod does not give up any of its charge. That is why induction gives the opposite sign to the rod.
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