Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o

Question

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -8q. Sphere B carries a charge of -1q. 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. Last, sphere C is touched to sphere B and separated from it. For the following questions, express your answers in terms of q.

(a) How much charge ends up on sphere C? Incorrect:

. (b) What is the total charge on the three spheres before they are allowed to touch each other? Incorrect:

(c) What is the total charge on the three spheres after they have touched?

Explanation / Answer

charge of A = qA = -8q

charege of B = qB = -1q

charge of C = qC = 0

IF A and B touched

charge on B = Q = (qA+qB)/2 = -4.5q

If C is touched to A

charge on C = charge on A = Q1 = (Q+qC)/2 = (-4.5+0)/2 = -2.25q

If C is touched to B

charge on C = charge on B = Q2 = (Q1+qB)/2 = (-2.25 - 4.5)*q/2 = -3.375 q

part a

charge on C = -3.375q

part b

Qtotal = -8-1 = -9 q

part c

Qtot = (-3.375 - 3.375-2.25) = -9q

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