9 The figure shows a section of a conducting rod of radius R

9. The figure shows a section of a conducting rod of radius R 3.10 mm and length L 1.10 m inside 10.0 mm and the same length L a thin-walled coaxial conducting cylindrical shell of radius R 14 C The net charge on the rod is Q1 +1.80 x 10 C; that on the shell is Q: 5.40 x 10 (a) (10 points) What is the magnitude of the electric field at radial distance r 15.0 mm? (b) (10 points) What is the magnitude of the electric field at radial distance r 7.50 mm? in nnints) What is the charge on the interior and exterior surfaces of the shell?

Solution

electric field is,

   E = Q/Ae0

      = [Q1-Q2] /[2*pi*r*L]e0

      = [1.8x10^-14 - 5.4x10^-14 ] / [2][pi][15X10^-3][1.1][8.85X10^-12]

     = -3.93e-2 N/C

Magnitude: E = 3.93e-2 N/C

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E = Q/Ae0

      = [Q2-Q1] /[2*pi*r*L]e0

      = [5.4x10^-14 -1.8x10^-14 ] / [2][pi][7.5X10^-3][1.1][8.85X10^-12]

     = 7.85e-2 N/C

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Charge on the interior surface of the shell: charge= -Q1 = 1.8x10^-14 C

Charge on the exterior surface of the shell: charge= Q1-Q2 = -3.6x10^-14 C