Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o
ID: 1661950 • Letter: C
Question
Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -8q. Sphere B carries a charge of -9q. 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?
(c) What is the total charge on the three spheres after they have touched?
Explanation / Answer
a)
Qa = charge on sphere A = - 8 q
Qb = charge on sphere B = - 9 q
Qc = charge on sphere C = 0
After Spheres A and B are touched together
Q'= Charge on A = Charge on B = (Qa + Qb)/2 = ((- 8 q) + (- 9 q))/2 = - 8.5 q
After Spheres A and C are touched together
Q'' = (Q' + Qc)/2 = (- 8.5 q + 0)/2 = - 4.25 q
After Spheres B and C are touched together
Q''' = (Q' + Q'')/2 = (- 8.5 q - 4.25 q)/2 = - 6.375 q
a)
charge on C = - 6.375 q
c)
total charge remains same = - 8 q - 9 q = - 17 q