Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o
ID: 1511234 • 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 -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
(a) We know that identical conducting spheres equalize their charge upon touching.
When the spheres A and B touch, an amount of charge +q ,flows from A to B to neutralize the -q charge on B leaving B momentarily neutral. Then the remaining amount of charge +5q on the sphere A is equally split between A and B i.e A and B hold each with equal amount of charge +2.5q
In next task when sphere C touched with Sphere A , The +2.5q on A splits equally between the A and C, because C is intially neutral.So the spheres A and C hold each with equal amount of charge +1.25q
Lastly when sphere C touched with shere B, the total charge on the spheres equally distributed between them.
+2.5q on B and the +1.25q on C combine to give a total charge of +3.75q,which is then equally divided between the Spheres B and C, thus B and C are each left with an amount of charge +1.875q.
Therefore sphere C ends with an amount of charge equal to +1.875q
The ratio of the final charge on sphere C to q is 1.875
(b) The cahrge on the three spheres before they were touched,are +6q on A , -q on B and zero charge on C thus total charge on the spheres is +6q -q +0 = +5q
The ratio of the final total charge on the three spheres to q before touch is 5 .
(c)The cahrge on the three spheres after they were touched,are +1.25q on A , +1.875q on B and +1.875 charge on C thus total charge on the spheres is +1.25q +1.875q +1.875q = +5q
The ratio of the final total charge on the three spheres to q after touch is 5 .