Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o
ID: 2001699 • Letter: C
Question
Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +2q. Sphere B carries a charge of -q. 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. Lastly, sphere C is touched to sphere B and separated from it. (a) What is the ratio of the final charge on sphere C to q? What is the ratio of the final total charge on the three spheres to q (b) before they are allowed to touch each other and (c) after they have touched?
Explanation / Answer
Qa = +2q
Qb = -q
Qc = 0
A and B touched :
Q'a = (Qa + Qb) /2 = (2q + (-q))/2 = 0.5 q
Q'b = 0.5 q
Qc' = 0
C and A touched together :
Q''c = (Q'a + Qc' )/2 = (0.5q + 0)/2 = 0.25 q
Q''a = 0.25 q
Q''b = 0.5 q
C and B touched together :
Qc''' = (Q''c + Q''b) /2 = (0.25q + 0.5 q)/2 = 0.375 q
Qb''' = 0.375 q
Q'''a = 0.25 q
a)
before allowed to touch
Qa /q = 2
Qb /q = -1
Qc /q = 0
after allowed to touch
Qc''' /q = 0.375
Qb''' /q = 0.375
Qa''' /q = 0.25