The figure is a section of a conducting rod of radius R_1 = 1.20 mm and length L

Question

The figure is a section of a conducting rod of radius R_1 = 1.20 mm and length L = 11.90 m inside a thin-walled coaxial conducting cylindrical shell of radius R_2 = 10.0R_1 and the (same) length L. The net charge on the rod is Q_1 = +3.44 times 10^-12 C; that on the shell is Q_2 = -2.05Q_1. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 2.22R_2? What are (c) E and (d) the direction at r = 5.03R_1? What is the charge on the (e) interior and (f) exterior surface of the shell?

Explanation / Answer

Gauss' Law,

integral of E.dA = Qin/ e0

(A) for r = 2.2R2

Qin = Q1 - 2.05Q1 = - 1.05Q1 = - 3.612 x 10^-12 C

E (2 pi r L ) = Qin/ e0

E (2 pi x 2.20 x 10 x 1.20x 10^-3 x 11.90 ) = (3.612 x 10^-12 ) / (8.854 x 10^-12)

E = 0.207 N/C

(B) Qin is negative hence radially inward.

(C) r = 5.03 r1

Qin = Q1 = 3.44 x 10^-12 C

E ( 2 x pi x 5.03 x 1.20 x 10^-3 x 11.90) = (3.44 x 10^-12) / (8.854 x 10^-12)

E = 0.86 N/C

(D)
Radially outward

(E) interior = - Q1 = - 3.44 x 10^-12 C

(F) exterior = Q2 - (- Q1) = -1.05Q1 = -3.612 x 10^-12 C

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