Question

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?

Answer 1

The final charge on sphere C is 2.5q. Before touching, the total charge is +5q, which remains the same after all interactions, demonstrating conservation of charge.

Step-by-step explanation:

When identical conductive spheres come into contact, the charges redistribute evenly across both spheres. If Sphere A is initially charged with +6q and Sphere B has a -q charge, touching them together allows their total charge to be shared, resulting in each sphere having (6q - q)/2 = 2.5q. After separation, both spheres A and B would have a charge of 2.5q. By touching Sphere C, which is uncharged, to A and then B in sequence, C gains a fraction of the charge from each, ending up with (2.5q)/2 from A and (2.5q)/2 from B, which totals 2.5q, since touching B does not change the charge obtained from A.

Before contact, the total charge is +5q (+6q from A and -q from B). After all the interactions, the total charge remains the same, +5q, but redistributed: A and B with 2.5q each and C with 2.5q.

In general, the total charge before and after remains constant, demonstrating conservation of charge.

Answer 2

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

Step-by-step 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

`q_A = + 6q`

`q_B = -q`

`q_c = 0`

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

so we have

`q_A' = q_B' = 2.5q`

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

so we have

`q_A'' = q_c' = 1.25q`

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

so we have

`q_c'' = q_b'' = 1.875q`