The figure is a section of a conducting rod of radius R1 = 1.30 mm and length L

Question

The figure is a section of a conducting rod of radius R1 = 1.30 mm and length L = 12.90 m inside a thin-walled coaxial conducting cylindrical shell of radius R2 = 13.1R1 and the (same) length L. The net charge on the rod is Q1 = +3.71 × 10-12 C; that on the shell is Q2 = -2.26Q1. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 2.03R2? What are (c) E and (d) the direction at r = 5.24R1? What is the charge on the (e) interior and (f) exterior surface of the shell?

Explanation / Answer

charge of conducting rod = Q1 = 3.71*10^-12 C

Radisu of rod R1 = 1.3 mm

length of rod, l = 12.9 m

charge of conducting shell = Q2 = -2.26*3.71*10^-12 C

Radius of shell R2 = 13.1*1.3 mm

length of shell, l = 12.9 m

A. Consider a gaussean surface at r = 2.03R2 ( outside the shell)

so, charge enclosed = (3.71)(1 - 2.26)*10^-12 C = -4.6746*10^-12 C

so electric field at this point is

From gauss' law

E*2*pi*2.03R2 = -4.6746*10^-12 / epsilon

E = -4.6746*10^-12 * 2* 8.98*10^9 / 2.03*13.1*1.3*10^-3 = -2.4285 V/m

B. Direction is radially inward ( -ve sign)

C. at r = 5.24 R1 ( inside the first shell)

Qen = Q1

so E = 2*Qen*k/5.24 R1 = 2*3.71*10^-12 * 8.98*10^9 / 5.24*1.3*10^-3 = 9.781 V/m

D. Direction radially outward, as +ve sign

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