Consider three identical metal spheres, A, B, and C. Sphere Acarries a charge of

Question

Consider three identical metal spheres, A, B, and C. Sphere Acarries a charge of +2q. Sphere B carries a charge of-q. Sphere C carries no net charge. Spheres A and B aretouched together and then separated. Sphere C is then touched tosphere A and separated from it. Lastly, sphere C is touched tosphere B and separated from it.

(a) What is the ratio of the final charge on sphere C toq?
(b) What is the ratio of the final total charge on thethree spheres to q? Consider three identical metal spheres, A, B, and C. Sphere Acarries a charge of +2q. Sphere B carries a charge of-q. Sphere C carries no net charge. Spheres A and B aretouched together and then separated. Sphere C is then touched tosphere A and separated from it. Lastly, sphere C is touched tosphere B and separated from it.

(a) What is the ratio of the final charge on sphere C toq?
(b) What is the ratio of the final total charge on thethree spheres to q?

Explanation / Answer

When two identical spheres are touched, the charge willequally distribute upon them. Initially, we have: A =+2q           B =-q          C =0 When A and C are touched, they each acquire a charge of (2q +0)/2 = q, so now they have charges of: A =+q             B= -q          C =+q When B and C are touched, they each acquire a charge of (-q +q)/2 = 0, so now they have charges of: A =+q            B =0           C = 0 a) The ratio of the final charge on sphere C to q is equal to0/q = 0. b) The ratio of the final total charge on the three spheres toq is equal to (q + 0 + 0)/q = 1.

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