Question

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -2q. Sphere B carries a charge of +3q. 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. Lastly, sphere C is touched to sphere B and separated from it.

(a) How much charge ends up on sphere A?
q
(b) How much charge ends up on sphere B?
q
(c) How much charge ends up on sphere C?
q
What is the total charge on the three spheres
(b) before they are allowed to touch each other and
q
(c) after they have touched?
q

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 + 3q)/2 = q/2

Now when C and A are touched, After separating

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

Now when C and B are touched, After separating

Charge on B = Charge on C = (qb + qc)/2 = ((q/2) + (q/4))/2 = 3q/8

Part A

final charge on Sphere A = q/4

Part B

final charge on Sphere B = 3q/8

Part C

final charge on Sphere C = 3q/8

Part D

Before touching total charge = qa + qb + qc = -2q + 3q + 0 = q

After touching total charge = qa + qb + qc = q/4 + 3q/8 + 3q/8 = 8q/8 = q

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