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 R1 = 1.20 mm and length L = 11.40 m inside a thin-walled coaxial conducting cylindrical shell of radius R2 = 10.8R1 and the (same) length L. The net charge on the rod is Q1 = +3.70 × 10-12 C; that on the shell is Q2 = -2.31Q1. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 2.02R2? What are (c) E and (d) the direction at r = 5.22R1? What is the charge on the (e) interior and (f) exterior surface of the shell?

Explanation / Answer

(a)

At distance r = 2.02R2

Qenclosed = Q1 + Q2

Qenc = Q1 - 2.32Q1 = -4.84*10^(-12) C

From gauss's law,

E.A = Qenc / e0

E = Qenc / 2*pi*r*l*e0

E = 4.84*10^(-12) / 2*3.14*2.02*10.8*1.20*10^(-3)*11.4*8.85*10^(-12)

E = 0.292 N/C

(b)

Direction is radially inwards.

(c)

At t = 5.22R1

Qenc = Q1

E = Q1 / 2*pi*r*l*e0

E = 3.70*10^(-12) / 2*3.14*5.22*1.20*10^(-3)*11.4*8.85*10^(-12)

E = 0.932 N/C

(d)

Direction is radially outward.

(e)

Charge on interior,

Qin = -Q1

Qin = -3.70*10^(-12) C

(f)

Charge on exterior-

Qex = Q1 + Q2

Qex = -1.31*3.7*10^(-12)

Qex = 4.84*10^(-12) C

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