Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o
ID: 1518454 • Letter: C
Question
Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -6q. 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 eneds up on sphere C? ______
(b) What is the total charge on the three spheres before they are allowed to touch each other? _____
(c) What is the total charge on the three spheres after they have touched? _____
Explanation / Answer
When two spheres touch, they distribute their charge evenly so that the charge on both are equal and add up to the original total charge.
=> So when A and B touch, they end up with the average of their charges: (-9q -6q) / 2 = -7.5q each.
=> When C and A touch, they each end up with (0q -7.5q) / 2 = -3.75q
=> Then, when C and B touch, they each end up with (-3.75q -7.5q) / 2 = -5.625q
a) charge ends up on sphere C = -5.625q
b) total charge on the three spheres before they are allowed to touch each other = - 15q
c) total charge on the three spheres after they have touched = -15q