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

Here,

initially

qAi = 5 q

qBi = -q

qCi = 0

when A and B are touched

qA = (5q - q)/2

qA = 2q

qB = 2 q

when C and A are touched

qA = (2q+0)/2

qA = q

qB = q

when C and B are touched

qB = (q + 2q)/2 = 1.5 q

qC = 1.5 q

for the final charges on spheres

qA = q

qB = 1.5 q

qC = 1.5 q

a)

Now ,

ratio of final charge on C to q = 1.5

b)

before tocuhing the spheres

ratio of total charge to q = (5 - 1 + 0)

ratio of total charge to q = 4

c)

after the touching

ratio of total charge to q = 1 + 1.5 + 1.5

ratio of total charge to q = 4

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