Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o
ID: 1417244 • Letter: C
Question
Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +7q. 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
Charge flow from one sphere to another until an equilibrium is reached
Sphere A and B are touched
Sphere A and B will have the same charge +3 q
Sphere C is touched to sphere A .Sphere C is charge less .The final charge will be 3/2 q
Finally sphere B is touched to sphere C ,The final charge on C and B will be (3/2 + 3)q /2 = (9 /4) q
The final charges on the spheres are
charge on C is (9/4)q
Charge on B is (9/4) q
Charge on A is (3/2) q
a) The ratio of final charge on C to q is = 9/4
b) The final total charge on the three spheres before they touch
7 q (on A) + - q (on B) + 0 q (on C) = 6q
c) After they have touched
(9/4) q (on C) + (9/4) q (on B) + (3/2) q (on B) = 6 q
Thus the total charge remains the same , no charge is created nor destroyed