In Figure 24-56a, we move an electron from an infinite distance to a point at di

Question

In Figure 24-56a, we move an electron from an infinite distance to a point at distance R = 4.40 cm from a tiny charged ball. The move requires work W = 1.81 x 10–13 J by us. (a) What is the charge (in C) Q on the ball? In Figure 24-56b, the ball has been sliced up and the slices spread out so that an equal amount of charge is at the hour positions on a circular clock face of radius R = 4.40 cm. Now the electron is brought from an infinite distance to the center of the circle. (b) With that addition of the electron to the system of 12 charged particles, what is the change in the electric potential energy of the system?

Explanation / Answer

(a) the work done results in a potential energy gain          W = qV              = (-e)( Q/40R) where R = 4.4cm= 0.044m W = 1.81 * 10-13 J      W= (-e) 9 * 109 Q/R     Q = WR/(-e) * 9* 109         = - 5.5 * 10-6C (b)         = - 5.5 * 10-6C (b)        the work is the same so increase in potential energy is U = 1.81 * 10-13 J

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