An infinite line of charge with linear density λ1 = 6 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.6 cm and outer radius b = 4.2 cm. The insulating shell is uniformly charged with a volume density of rho = - 634 μC/m3. What is λ2, the linear charge density of the insulating shell?

Answer: λ2 = 2.34 * 10^-6 C/m

Explanation: In order to calculate the value of the linear charge density of the insulating shell we have to multiply ρ * Volume of the hollow cylinder, so

Volume of cylinder:2*π*b*L * (b-a) where (b-a) is the thickness, then

λ2=Q/L = 634 * 10^-6 C/m^3 * 2*π*0.042 m * (0.042-0.26) = = 2.34 μ C/m