How much of the charge ends up on sphere C? Answers: a.1.5q b. 4p c. 4q Three id

Question

How much of the charge ends up on sphere C?

Answers:

a.1.5q

b. 4p

c. 4q

Three identical metal spheres. A, B, and C initially have net charges as shown. Spheres A and B are now touched together and then separated. Then, sphere C is touched and then separated from to sphere A. Lastly, sphere C is touched and then separated from to sphere B. (a) How much charge ends up on sphere C? What is the total charge on the three spheres (b) before they are allowed to touch each other and (c) after they have touched?

Explanation / Answer

At first charges are distributed like this
A = +5q, B = -1q, C = 0
Then you touch A and B => 5q - 1q = 4q
The charge is equally distributed over both spheres so you end up with
A = 2q, B = 2q, C = 0
Next you touch C to A
2q + 0 = 2q
A = 1q, B = 2q, C = 1q
Then C is touched to B
1q +2q = 3q
A = 1q, B = 1.5q, C = 1.5q

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