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 +5q. Sphere B carries a charge of -q. 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) What is the ratio of the final charge on sphere C to q? What is the ratio of the final total charge on the three spheres to q (b) before they are allowed to touch each other and (c) after they have touched?

Explanation / Answer

Initially charge on spehere

Qa1 = +5q

Qb1 = -q

Qc1 = 0

when A and B touched together

Sphere A and B will have same charge

Qa2 = Qb2 = (Qa1 + Qb1)/2

Qa2 = (+5q - q)/2

Qa2 = +2q

Qb2 = +2q

Qc2 = 0

when A and C touched

Qa3 = Qc3 = (Qa2 + Qc2)/2

Qa3 = (+2q + 0)/2

Qa3 = +q

Qb3 = +2q

Qc3 = +q

Then B and C touched

Qb4 = Qc4 = (Qb3 + Qc3)/2

Qa4 = +q

Qb4 = (+2q + q)/2

Qb4 = +1.5 q

Qc4 = +1.5 q

A.

ratio of charge on C/q = Qc4/q

ratio = 1.5*q/q

ratio = 1.5

B.

Before touching

Initially total charge = +5q -q + 0 = +4q

ratio = Qt/q = +4q/q

ratio = 4

C.

After touching

Qt = +q + 1.5q + 1.5q = +4q

ratio = Qt/q = +4q/q

ratio = 4

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