A thin, cylindrical plastic rod is rubbed with fur, which leaves it with a unifo

Question

A thin, cylindrical plastic rod is rubbed with fur, which leaves it with a uniformly distributed charge of Q = +80 nC. The rod lies on the x-axis, with its ends at (-0.12, 0, 0) m and (+0.12, 0, 0) m. The radius of the rod is 0.002 m. How many fewer electrons than protons are in/on this charged rod? What is the electric field due to this charged rod at (0, 0.16, 0) m? A steel ball of radius 0.02 m, which carries zero net charge, is located near the charged rod, with its center at (0.03, -0.04, 0) m. What is the net electric field at the center of the steel ball? Sketch the polarization of the ball.

Explanation / Answer

a)

Q = n e

80 x 10-9 = n (1.6 x 10-19)

n = 5 x 1011 C

b)

L = length of rod = 0.24 m

r = distance from rod = 0.16 m

electric field by rod is given as

E =2kQ /(r sqrt(L2 + 4r2))

E = 2 (9 x 109) (80 x 10-9) /((0.16) sqrt((0.24)2 + 4 (0.16)2))

E = 22500 N/C

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