Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o
ID: 2116284 • Letter: C
Question
Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +3q. 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
Initial charges : sphere A = 3q , B = -q , C = 0
Now A and B are touched together so charges are : A = B= (3q-q)/2 = 2q/2 = q . Sphere C is touched with sphere A so charges are A = C = q+0/2 = q/2
Sphere C is touched with sphere B so charges are : C = B = (q + q/2)/2 = 3q/4
Ratio of final charge on sphere C to q = 3q/4/q = 3/4
total charge before touching = 3q - q + 0 = 2q
total charge after touching = q/2 + 3q/4 + 3q/4 = 2q
So ratio = 2q/2q = 1