A long nonconducting cylinder has a charge density p=ar where a =4.96 C/m^4 and

Question

A long nonconducting cylinder has a charge density p=ar where a =4.96 C/m^4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell. What is the electric field at 2 cm from the central axis. Assume the length is very long compared to the diameter of the shell and neglect edge effects. Answer in units of N/C A long nonconducting cylinder has a charge density p=ar where a =4.96 C/m^4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell. What is the electric field at 2 cm from the central axis. Assume the length is very long compared to the diameter of the shell and neglect edge effects. Answer in units of N/C A long nonconducting cylinder has a charge density p=ar where a =4.96 C/m^4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell. What is the electric field at 2 cm from the central axis. Assume the length is very long compared to the diameter of the shell and neglect edge effects. Answer in units of N/C

Explanation / Answer

Given,

Charge density, = r

= 4.96 C/m4, r1 = 2 cm = 0.02 m

From Gauss's law,

E x 2r1 x L = (1/0) x 2rL dr (from 0 ro r1)

E x r1 = (/0)r2 dr (from 0 ro r1)

E x r1 = (/0)r13/3

E = r12/(30) = (4.96 x 0.022) / (3 x 8.85 x 10-12) =  7.47 x 107 N/C

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