Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +3q....

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?

Solutions

Expert Solution

When spheres A is touched to sphere B, then their total charge will be given as :

(+3q) + (-q) = +2q

The total charge is equally divided between them. So, they will each have a charge of '+q'.

When sphere C is touched to sphere A, then their total charge will be given as :

(+q) + (0 q) = +q

The total charge is equally divided between them. So, they will each have a charge of '+0.5q'.

When sphere C is touched to sphere B, then their total charge will be given as :

(+0.5q) + (+q) = +1.5q

The total charge is equally divided between them. So, they will each have a charge of '+0.75q'.

In the end, A has "+0.5q", B has "+0.75q" and C has "+0.75q".

(a) What is the ratio of the final charge on sphere C to q?

Ratio : (+0.75q) / (q) = +0.75

(b) What is the ratio of the final total charge on the three spheres to q before they are allowed to touch each other?

We know that, q_A + q_B + q_C

(+3q) + (-q) + (0q) = +2q

Ratio : (+2q) / q = +2

We know that, q_A + q_B + q_C

(+0.5q) + (+0.75q) + (+0.75q) = +2q

Ratio : (+2q) / q = +2

genius_generous answered 9 months ago

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