Three similar metal spheres of the same radius and mass on insulated stands are

Question

Three similar metal spheres of the same radius and mass on insulated stands are initially charged as follows: sphere A has +6.0 nC charge, sphere B has –2.0 nC of charge, and sphere C is neutral.
In this order, the spheres are touched for long enough for the charges to come to equilibrium and then separated again. Sphere A contacts B (and then separates.) Sphere A then touches C (and then separates.) Sphere C then touches B (and then separates.) After all this touching and separating, what is the charge on each sphere? Show that the total charge at the beginning and at the end has not changed (that is, that charge is conserved.)

Explanation / Answer

Initailly, QA = +6 nC

QB = -2 nC

QC = 0

initail total charge = 6-2+0 = 4 nC

step 1) when A and B touches each other

QA = (6-2)/2 = 2 nC

QB = (6-2)/2 = 2 nC

step 2) when A and C touches each other

QA = (2+0)/2 = 1 nC

QC = (2+0)/2 = 1 nC

step 3) when B and C touches each other

QB = (2+1)/2 = 1.5 nC

QC = (2+1)/2 = 1.5 nC

so, finally, QA = 1 nC, QB = 1.5 nC, QC = 1.5 nC

finaltotal charge = 1 + 1.5 + 1.5 = 4 nc

so, total initial charge = total final charge

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