Shown below are three identical metal spheres, A, B and C. Sphere A carries a ch

Question

Shown below are 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. Consider the following steps: (i) sphere A and B are touched together and then separated, (ii) Next, sphere C is then touched to sphere A and separated from it. (iii) Sphere C is touched to sphere B and separated from it. Explain in one or two sentences together with diagrams that illustrate the processes (i) to (iii), how much charge ends up on sphere C? Explain in one or two sentences, what is the total charge on the three spheres before and after they are touched.

Explanation / Answer

Let Qa, Qb and Qc be charges on three spheres. When two metal bodies are bring in contact the charges redistribute and each of them carry equal charges, and total charge remain same.

Initially Qa = +5q, Qb = -q, Qc = 0.

step 1) Sphere A and B are touched, Qa+Qb = 5q - q = 4q will be divided equally i.e. each of them will carry +2q charge. Hence after step 1, Qa = 2q, Qb = 2q and Qc = 0.

step2) Sphere A and C are touched. Qa + Qc = 2q + 0 = 2q will be divided equally. .

Hence after step 2, Qa = q , Qb = 2q, Qc = q.

step 3) Sphere B and C are touched. Qb + Qc = 2q + q = 3q.(divided equally)

after step 3, Qa = q, Qb = 3q/2 and Qc = 3q/2.

Hence final charge on Sphere C is 3q/2.

b) Initial total charge = Qa + Qb + Qc = 5q - q + 0 = 4q

Final total charge = Qa + Qb + Qc = q + 3q/2 + 3q/2 = 4q.

Hence total charge is conserved.

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