A long cylindrical conducting shell has inner radius R1=10 cm and an outer radiu

Question

A long cylindrical conducting shell has inner radius R1=10 cm and an outer radius R2=12 cm. the conductor has no net charge. At the center of the cylinder, there is a negative line of charge with linear charge density =5c/m.

A)     Find the magnitude and direction of the electric field outside the shell at a distance r from the center, (r>R2)

B)      Find the magnitude and direction electric field in the region between the inner and the outer radius of the conductor at distance r from the center (R2> r >R1)

C)      Find the surface charge density on the outer surface of the conductor.

Explanation / Answer

Given that Inner radius of the cylinder R1 = 10*10^-2 m Outer radius of the cylinder R2 = 12*10^-2 m Linear charge density () = 5*10^-6 C/m. (A) Electricfield out side the cylinder E = (/2_0R1)                                                                                                          = (5*10^-6/2*3.14*8.89*10^-12*10*10^-12)                                                                                                          = 8.9*10^15 N/C (B) Electric field in between the two shells E = (R1/2_0(R2-R1)^2)                                                               = [(5*10^-6)(10*10^-12)/2*3.14*8.89*10^-12(12*10^-12-10*10^-12)                                                              = 3.9*10^6 N/C (C) E = /o        where o = Permittivity of free space = 8.85*10^-12 C^2/N m^2 = Eo    = (8.9*10^15 ) (8.85*10^-12 )    = 78.76*10^3 C/m^2 (A) Electricfield out side the cylinder E = (/2_0R1)                                                                                                          = (5*10^-6/2*3.14*8.89*10^-12*10*10^-12)                                                                                                          = 8.9*10^15 N/C (B) Electric field in between the two shells E = (R1/2_0(R2-R1)^2)                                                               = [(5*10^-6)(10*10^-12)/2*3.14*8.89*10^-12(12*10^-12-10*10^-12)                                                              = 3.9*10^6 N/C (C) E = /o        where o = Permittivity of free space = 8.85*10^-12 C^2/N m^2 = Eo    = (8.9*10^15 ) (8.85*10^-12 )    = 78.76*10^3 C/m^2 Electric field in between the two shells E = (R1/2_0(R2-R1)^2)                                                               = [(5*10^-6)(10*10^-12)/2*3.14*8.89*10^-12(12*10^-12-10*10^-12)                                                              = 3.9*10^6 N/C (C) E = /o        where o = Permittivity of free space = 8.85*10^-12 C^2/N m^2 = Eo    = (8.9*10^15 ) (8.85*10^-12 )    = 78.76*10^3 C/m^2 E = /o        where o = Permittivity of free space = 8.85*10^-12 C^2/N m^2 = Eo    = (8.9*10^15 ) (8.85*10^-12 )    = 78.76*10^3 C/m^2

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