Question

The figure is a section of a conducting rod of radius R₁ = 1.45 mm and length L = 12.60 m inside a thin-walled coaxial conducting cylindrical shell of radius R₂ = 10.7R₁ and the (same) length L. The net charge on the rod is Q₁ = +3.56

Answer 1

Given that conducting rod of radius R_1 = 1.45 mm

                                             radius R_2 = 10.7 R_1

a ) The flux through this surface is ? = 2?rLE

                     E = Q_enc / 2??_0 L r

          = - 3.56 *10^-12 C / 2? * 8.85 *10^-12 * 12.6m * 10.7 (1.45 *10^-3 m )

         = -0.327 N/C

          = 0.327 N/C

b ) Negative sign indicates that field points inward

c ) Magnitude of electric field is   E = Q_enc / 2??_0 L r  

                               = 3.56 *10^-12 C / 2? * 8.85 *10^-12 * 12.6m * 5.11 (145 *10^-3 m )

                               = 0.686 N/C

d ) The positive sign indicates field points outward

e ) The inner surface of the shell has Q_in = - Q_1

                                                                  = - 3.56 *10^-12 C

f ) The outer shell has Q_out   = Q_2 - Q_in = - Q_1

                                                 = - 3.56*10^-12 C