An infinitely long uniform line of charge with λ = 6x10^-6 C/m runs along the axis of an infinitely long thin cylindrical nonconducting plastic shell of radius a1 = 0.2 m which has a uniform surface charge density σ = 6x10^-6 C/m^2. Concentric with the plastic shell, there is an infinitely long thick conducting cylindrical shell with inner radius a2 = 0.4 m and outer radius a3 = 0.5 m on which there is no net charge.

a. Find the charge per unit length on the plastic shell. Calculate the eletric field at the given values of r, where r is the distance from the line of charge.

b. At r = 0.1 m

c. At r = 0.3 m

d. At r = 0.45 m

e. At r = 0.6 m

f. Find the surface charge densities on the inner and outer surfaces of the conductor.