Consider 3 identical metal spheres A,B and C. A carries a charge of +5q b carries a charge of -q and C carries no net charge. Sphere A and B are touched together and then separated. C is then touched to A and separated from it.

Lastly C is touched to B and separated from it.

How many charge (if any) ends up on charge C?

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The scenario you are describing involves the interaction of three identical metal spheres: A, B, and C. Sphere A carries a charge of +5q, sphere B carries a charge of -q, and sphere C carries no net charge initially.

Let's go step by step through the process you mentioned:

1. A and B are touched together and then separated:
When spheres A and B are brought into contact and then separated, some charge transfer occurs between them. Since metals are good conductors, the charges redistribute themselves to reach equilibrium. However, since sphere A has a higher positive charge (+5q) compared to sphere B (-q), some of sphere A's positive charge will transfer to sphere B, equalizing the charges to some extent.

To understand the final charge distribution after they are separated, you'll need to know the specific charge distribution on each sphere before they are touched. Without that information, we cannot precisely determine the exact charges on spheres A and B after contact and separation, even though we know that some charge transfer has occurred.

2. C is then touched to A and separated from it:
In this step, sphere C is touched to sphere A and then separated. Since sphere A had a charge of +5q, touching it with sphere C allows charge transfer between them due to conduction.

If we assume that sphere C initially carries no net charge, touching it to sphere A will result in charge redistribution. Sphere C will acquire some of the positive charge from sphere A. However, without knowing the initial charge on sphere C before contact, it's difficult to determine the precise charges on both spheres after separation.

In summary, the charge distribution on spheres A, B, and C after the mentioned procedures can only be determined if we have information about their initial charges (or ratios of their initial charges). Without that information, we can only infer that some charge transfer occurred, but we cannot determine the exact final charges on the spheres.