Scenario 1:
Remember whenever metal spheres are touched, the charge is equally distributed between them. now
When A and B are touched, After separating
Charge on A = Charge on B = (qa + qb)/2 = (+Q+ 0)/2 = Q/2
Now when C and A are touched, After separating
Charge on A = Charge on C = (qa + qc)/2 = ((Q/2) + 0)/2 = Q/4
Now when A and D are touched, After separating
Charge on A = Charge on D = (qa + qd)/2 = ((Q/4) + 0)/2 = Q/8
So,
Final Charge on sphere A = QA = (1/8)*Q
Scenario 2:
Remember whenever metal spheres are touched, the charge is equally distributed between them. now
When A and B are touched, After separating
Charge on A = Charge on B = (qa + qb)/2 = (+Q+ 0)/2 = Q/2
Now when C and B are touched, After separating
Charge on B = Charge on C = (qb + qc)/2 = ((Q/2) + 0)/2 = Q/4
Now when C and D are touched, After separating
Charge on C = Charge on D = (qc + qd)/2 = ((Q/4) + 0)/2 = Q/8
So, Since Sphere A is not used in 2nd and 3rd step, So from step 1, charge on sphere A will be
Final Charge on Sphere A = QA = (1/2)*Q
Scenario 3:
Remember whenever metal spheres are touched, the charge is equally distributed between them. now
When A and D are touched, After separating
Charge on A = Charge on D = (qa + qd)/2 = (+Q+ 0)/2 = Q/2
Now when C and D are touched, After separating
Charge on D = Charge on C = (qd + qc)/2 = ((Q/2) + 0)/2 = Q/4
Now when A and D are touched, After separating
Charge on A = Charge on D = (qa + qd)/2 = ((Q/2) + (Q/4))/2 = 3Q/8
Now when A and B are touched, After separating
Charge on A = Charge on B = (qa + qb)/2 = ((3Q/8) + 0)/2 = 3Q/16
So,
Final Charge on Sphere A = QA = (3/16)*Q
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