The figure below shows four identical conducting spheres that are actually well

Question

The figure below shows four identical conducting spheres that are actually well separated from one another. Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of -32e) and then they are separated. Finally, sphere W is touched to sphere C (with an initial charge of +52e), and then they are separated. The final charge on sphere W is +14e. What was the initial charge on sphere A?
answer: _________e

Explanation / Answer

we have four sphere namely W, A, B, and C and also

given at the start that

qW = 0, qA=?, qB = -32e, qC = 52e

and at the end of the process qW=14 e.

Now each time W touches another sphere than has some charge not equal to that on W the charges move so that each sphere has an equal net charge. So let's start:

When W touches A --> qW = qA/2 since W had zero charge to start it gets 1/2 the charge on A

W touches B ---> qW = 1/2(qW + qB) = 1/2(qA/2 -32) = qA/4 - 16

W touches C --> qW = 1/2(qW + qC) = 1/2(qA/4 -16 + 52)

= qA/8 +36/2 = 14 since this is the final charge.

Now solve for qA

qA/8 = 14 - 18

qA/8 = -4

qA = -32 e-------------------<<<<<<<<Answer

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