2) Consider three identical metal spheres, A, B, and C. Sphere A carries a charg

Question

2) Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +7 uC. Sphere B carries a charge of . 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. (a) How much charge ends up on sphere C? What is the total charge on the three spheres (b) before they are allowed to touch each other and (c) after they have touched?

Explanation / Answer

a)

When two spheres touch, they distribute their charge evenly so that the charge on both are equal and add up to the

original total charge.

So when A and B touch, they end up with the average of their charges : (7q + -q) / 2 = 3q each.

When C and A touch, they each end up with (0q + 3q) / 2 = 1.5q.

Then, when C and B touch, they each end up with (3q + 1.5q) / 2 = 2.25q     

(b)

Total charge = 7q - 1q = 6q

c)

Total charge = 3q + 1.5q + 2.25q = 6.75q

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