Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o

Question

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +10q. Sphere B carries a charge of -7q. Sphere C carries no net charge. Spheres A and B are touched together and then separated. Sphere C is then touched to sphere A and separated from it. Last, sphere C is touched to sphere B and separated from it. For the following questions, express your answers in terms of q. (a) How much charge ends up on sphere C? (b) What is the total charge on the three spheres before they are allowed to touch each other? (c) What is the total charge on the three spheres after they have touched?

Explanation / Answer

The problem can be solved as follows:

Since the spheres are identical , the charge would be distributed equally between 2 spheres when touched.

Hence :

1. A -> B => QA = QB = (10q + 3q)/2 = 6.5q

2. A -> C => QA = QC = (6.5q + 0)/2 = 3.25q

3. B -> C => QB = QC = (3.25q + 6.5q)/2 = 4.875q

Thus:

A) C ends up with a charge of 4.875q.

B) 10q + 3q = 13q

C) 3.25q + 4.875q + 4.875q  = 13q

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