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

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Answer:

Part a)

Final charge on C : q = 1.875

Part b)

Ratio for A = 6 : 1.25

Ratio for B = -1 : 1.875

Ratio for C = 0

Explanation:

When two identical metal sphere are connected together then the charge on them will get equally divided on both after connecting them by conducting wire

So here we have

[tex]q_A = + 6q[/tex]

[tex]q_B = -q[/tex]

[tex]q_c = 0[/tex]

Step 1: We connected A and B and then separate them

so we have

[tex]q_A' = q_B' = 2.5q[/tex]

Step 2: We connected A and C and then separate them

so we have

[tex]q_A'' = q_c' = 1.25q[/tex]

Step 3: We connected B and C and then separate them

so we have

[tex]q_c'' = q_b'' = 1.875q[/tex]

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