Question

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +9q. 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?

Answer 1

Law of Conservation of Charge is applicable here;

a) A and B are touched together and then separated

Qa = 4q, Qb = 4q;

Sphere C is then touched to sphere A and separated from it

Qc = 2q, Qa = 2q

finally sphere C is touched to sphere B and separated from it

Qc = 3q, Qb = 3q   

therefore final charge on A, B and C sphere is;

Qa = 2q , Qb = 3q and Qc = 3q. (you can find the ratio)

a) ratio of the final charge on sphere C to q

Qc/q = 3q/q = 3.

What is the ratio of the final total charge on the three spheres to q

Q = Qa + Qb + Qc =8q

Q/q = 8q/q = 8.

b) before they are allowed to touch each other

Qa/q = 9q/q = 9;

Qb/q = - q/q = -1

Qc/q = 0

c)  they have touched

Qa/q = 2q/q = 2;

Qb/q = 3q/q = 3;

Qc/q = 3q/q = 3.