Figure 23-38 is a section of a conducting rod of radius R1 = 1.46 mm and length

Question

Figure 23-38 is a section of a conducting rod of radius R1 = 1.46 mm and length L = 11.20 m inside a thin-walled coaxial conducting cylindrical shell of radius R2 = 12.3R1 and the (same) length L. The net charge on the rod is Q1 = +3.73 × 10-12 C; that on the shell is Q2 = -2.33Q1. What are the (a) magnitude E and (b) direction (radially inward (type 1) or outward (type 0)) of the electric field at radial distance r = 2.04R2? What are (c)E and (d) the direction (1 for inward, 0 for outward) at r = 5.10R1? What is the charge on the (e) interior and (f) exterior surface of the shell?

Give electric fields in N/C and charges in Coulombs.

http://edugen.wiley.com/edugen/courses/crs4957/art/qb/qu/c23/pict_23_27.gif

Explanation / Answer

Given that conducting rod of radius R_1 = 1.46 mm                                              radius R_2 = 12.3 R_1 Length L = 11.20 m Net charge Q_1 = + 3.73*10^-12 C , Q_2 = - 2.33 Q_1 a ) The flux through this surface is = 2rLE                      E = Q_enc / 2_0 L r           = - 3.73 *10^-12 C / 2 * 8.85 *10^-12 * 11.2m * 12.3 (1.46 *10^-3 m )          = -0.33 N/C           = 0.33 N/C b ) Negative sign indicates that field points inward c ) Magnitude of electric field is   E = Q_enc / 2_0 L r                                  = 3.73 *10^-12 C / 2 * 8.85 *10^-12 * 11.2m * 5.1 (1.46 *10^-3 m )                                = 0.804 N/C d ) The positive sign indicates field points outward e ) The inner surface of the shell has Q_in = - Q_1                                                                   = - 3.73 *10^-12 C f ) The outer shell has Q_out   = Q_2 - Q_in = - Q_1                                                  = - 3.73 *10^-12 C

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