A long non-conducting cylinder [dark gray] has a charge density rho = alpha r, w

Question

A long non-conducting cylinder [dark gray] has a charge density rho = alpha r, where alpha = 4.21 C/m4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell (light gray in the figure below). What is the electric field at 1 cm from the central axis? Assume the length L is very long compared to the diameter of the shell, and neglect edge effects. Answer in units of N/C What is the electric field at 9.04 cm from the central axis? Answer in units of N/C What is the direction of the electric field at 14.4 cm from the central axis? The electric field is not a vector and therefore has no direction. Undetermined, since the field is zero. Points radially inward. Points radially outward. What is the electric field at 19.2 cm from the central axis? Answer in units of N/C What is the surface charge density inside the hollow cylinder? Answer in units of C/m2

Explanation / Answer

1. E = r/20 = 4.21*0.01/2*8.85*10^-12 = 2.37 *10^9 N/C


2. E = 4.21*(9.04-4.46)/2*8.85*10-^-12 = 10.8 *10^8 N/C

3. radailly outward

4. E = 4.21*0.192/2*8.85*10-12 = 45.6 *10^9 N/c

5. surface charge density = *(r2-r1) = 4.21*0.059 = 0.25 C/m^2

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