Problems 6 and 7 Please Consider two spheres, sphere 1 having radius R1 = 5cm, a

Question

Problems 6 and 7 Please

Consider two spheres, sphere 1 having radius R1 = 5cm, and sphere 2 having a radius R2 = 15cm, separated from one another by a center-to-center distance of 10 m. The two are connected to each other by a thin wire that is broken open in the middle by a switch. Sphere 1 is charged to 1 nC, and sphere 2 is neutral. When the switch is connected, charge moves spontaneously from sphere 1 to sphere 2 untill equilibrium is reached. How much charge will be on each sphere when equilibrium is reached? (Assume that the charge is uniformly distributed on thier surfaces. Very little charge remains on the connecting wire because it is so thin. ) In problem 5, what is the minimum amount of work required to charge the capacitor is transferred. In problem 6, what is the maximum work that could be extracted from this process?

Explanation / Answer

6)
total charge, Q = 1 nC

q1+q2 = 1 n C --(1)

charge moves until the spheres get same potential

v1 = v2

k*q1/R1 = k*q2/R2

q1/5 = q2/15

q1 = 3*q2 --(2)

from equations 1 and 2

3*q2+ q2 = 1 nC

q2 = 1/4 *10^-9 = 0.25*10^-9 C

so, q1 = 1*10^-9 - 0.25*10^-9

q1 = 0.75*10^-9 C

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