An electron starts from rest 3.00 cm from the center of a uniformly charged insu

Question

An electron starts from rest 3.00 cm from the center of a uniformly charged insulating sphere of radius 2.00 cm and total charge 1.00 nC. What is the speed of the electron when it reaches the surface of the sphere?

Explanation / Answer

radius r = 2.0 cm, Q = 1.0 nC electron q = -1.6 x 10^-19 C, R = 3.0 cm > r , it moves OUTSIDE the sphere. The increase of the kinetic energy Ek of the electron comes from the decrease of potential energy Ep. initial Ep = kQq/R, where k = 9 x 10^9 final Ep = kQq/r the decrease of Ep = kQq/R - kQq/r = kQq(1/R - 1/r) = 9 x 10^9 x 1.0 x 10^-9 x (-1.6 x 10^-19) x (1/0.03 - 1/0.02) = 2.4 x 10^-17 J It equals its final Ek = 1/2*mv^2 so v = sqrt(2 x 2.4 x 10^-17/(9.1 x 10^-31)) = 7.3 x 10^6 m/s

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