Consider three identical metal spheres, A, B, and C. Sphere A carries a charge o

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?

Explanation / Answer

Here A= +9q , B=-q , C=0

Note that when two conducting spheres touch each other, the total charge from two conducting spheres redistributed between two spheres in such a way that each sphere has half the total charge.

Let us follow each step one by one,

Step1: When spheres A and B are touched together and then separated

(+9q+(-q))/2= 8q/2= 4q

Sphere A and B each will have charge 4q

Step 2: When sphere C is then touched to sphere A and separated from it

(+4q+(0q))/2= 4q/2= 2q

Sphere A and C each will have charge 2q

Step 3: When sphere C is then touched to sphere B and separated from it

(+4q+(2q))/2= 6q/2= 3q

Sphere A and C each will have charge 3q

Part a) The final charge on C = 3q

Hence,

The ratio of the final charge on sphere C to q = 1/3

Part b) Final total charge on the three spheres to q before they are allowed to touch each other

= A+B+C = +9q -q+ 0 = 8q

Ratio = 8

Part c) Final total charge on the three spheres to q after they have touched

= A+B+C = 2q+3q+3q = 8q

Ratio = 8

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