The figure is a section of a conducting rod of radius = 1.40 mm and length L = 1

Question

The figure is a section of a conducting rod of radius = 1.40 mm and length L = 12.90 m inside a thin-walled coaxial conducting cylindrical shell of radius R_2 = 10.8R_1 and the (same) length L. The net charge on the rod is Q_1 = +3.51 times 10^-12 C: that on the shell is Q_2 = -2.11 Ohm. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 2.20 R_2? What are (c) E and (d) the direction at r = 5.14 R_1? What is the charge on the (e) interior and (f) exterior surface of the shell?

Explanation / Answer

from Gauss law,

net flux = Qin / e0

E ( 2 pi r L ) = Qin / e0

(A) for r = 2.20 R2

Qin = Q! = Q2 = Q - 2.11Q1 = - 1.11 Q1

Qin = 3.90 x 10^-12 C

E (2 pi (2.20 x 10.8 x 1.40 x 10^-3))(12.90) = 3.90 x 10^-12 / (8.854 x 10^-12)

E = 0.163 N/C

(B) inwards (Qin is negative)

(C) r = 5.14 r1 ; Qin = 3.51 x 10^-12

E (2 x pi x 5.14 x 1.40 x 10^-3)(12.90) = (3.51 x 10^-12) / (8.854 x 10^-12)

E = 0.678 N/C

(D) Outward

(E) interior surface charge = - Q1 = - 3.51 x 10^-12 C

(F) exterior surface charge = Q2 + Q1 = 1.11Q1 = 3.90 x 10^-12 C

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