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?

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

d is the correct answer