Answer to Question #162224 in Physics for Pixis

Question

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Sphere A (8q) touched Sphere B (12q) then separated. Sphere A touched Sphere C (-5q) then separated.

a) What is the Σq on the three spheres before touching each other?

b) What are the final charges on each sphere, assuming they are identical in radius, which is r?

Answer 1

(a)

$$Q_{tot}=Q_A+Q_B+Q_C=8q+12q-5q=15q.$$

(b) When sphere A is touched to sphere B, the net charge on each of them equals:

$$Q=\dfrac{Q_A+Q_B}{2}=\dfrac{8q+12q}{2}=10q.$$

Then, sphere A is touched to sphere C, so the net charge on each of them equals:

$$Q=\dfrac{Q_A+Q_C}{2}=\dfrac{10q-5q}{2}=2.5q.$$

Therefore, each sphere has the following final charges:

$$Q_A=2.5q, Q_B=10q, Q_C=2.5q.$$