Question

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -6q. Sphere B carries a charge of +5q. 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?

(b) How much charge ends up on sphere B?

(c) 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?

Answer 1

initially

charge on sphere A , QA = -6 q

charge on sphere B , QB = +5 q

charge on sphere C , Qc = 0

Spheres A and B are touched together and then separated

charge on sphere A , QA' = charge on sphere B , QB' = (-6q + 5 q)/2 = -q/2

Sphere C is then touched to sphere A and separated from it

charge on sphere A , QA" = charge on sphere C, QC' = (-q/2 + 0)/2 = -q/4

sphere C is touched to sphere B and separated from it

charge on sphere C , QC" = charge on sphere B, QB" = (-q/4 - q/2)/2 = -3q/8

(a)

charge on sphere A , QA" = -q/4

(b)

charge on sphere B, QB" = -3q/8

(c)

charge on sphere C , QC" = -3q/8

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the total charge on the three spheres

(b) before they are allowed to touch each other

Qtotal = QA + QB + Qc = -6q + 5q + 0 = -q

(c)

after they have touched

Qtotal = QA" + QB" + QC" = -q/4 - 3q/8 - 3q/8

Qtotal = -q