Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o
ID: 2226913 • Letter: C
Question
Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -4q. Sphere B carries a charge of +5q. 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? (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: (-10q + 7q) / 2 = 1.5q each. When C and A touch, they each end up with (0q + 1.5q) / 2 = 0.75q. Then, when C and B touch, they each end up with (0.75q + 1.5q) / 2 = 1.125q. C has 1.125q of charge. (b) Total charge = 1.125q + 1.125q + 0.75q = 3q, which equals the total charge to begin with. This is conservation of charge.