Question

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -6q. Sphere B carries a charge of -5q. 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. Last, sphere C is touched to sphere B and separated from it. For the following questions, express your answers in terms of q. (a) How much charge ends up on sphere C? Incorrect: Your answer is incorrect. (b) What is the total charge on the three spheres before they are allowed to touch each other? Incorrect: Your answer is incorrect. (c) What is the total charge on the three spheres after they have touched?

Answer 1

Ans

The spheres are identical. Hence when two spheres are touched, total charge on them distributes equally on them.

a) i) Total charge on A + B = -6q + (-5q)= -11q, So after spheres have touched,

the charge on A = -11q/2 = -5.5q and charge on B = -11q/2 = -5.5q

ii) C is touched to A. Charge on A + C = -5.5q + 0= -5.5q, so charge on C = -5.5q/2 = -2.75q and charge on A = -2.75q

iii) Now C is touched to B. Total charge on B + C = -5.5q+(-2.75q) = -8.25q,

hence charge on C = -8.25q/2 = -4.125q and charge on B = -4.125q.

So C ends up with a charge of -4.125q

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b) Total charge on sphere before they are allowed to touch each other = -6q +(-5q)+ 0 = -11q

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c) Total charge on sphere after they have touched each other =

-2.75q +(-4.125q) + (-4.125q)= -11q

as expected from conservation of charge.