Question

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -2q. 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?

Answer 1

Remember whenever metal spheres are touched, the charge is equally distributed between them. now

When A and B are touched, After separating

Charge on A = Charge on B = (qa + qb)/2 = (-2q - 7q)/2 = -9q/2

Now when C and A are touched, After separating

Charge on A = Charge on C = (qa + qc)/2 = ((-9q/2) + 0)/2 = -9q/4

Now when C and B are touched, After separating

Charge on B = Charge on C = (qb + qc)/2 = ((-9q/2) + (-9q/4))/2 = -27q/8

Part A

final charge on Sphere C = -27q/8

Part B

Before touching total charge = qa + qb + qc = -2q - 7q + 0 = -9q

Part C

After touching total charge = qa + qb + qc = -9q/4 - 27q/8 - 27q/8 = -72q/8 = -9q

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