Problem 1 Consider a concentric cylindrical capacitor consisting of two thin cylindrical metallic shells of radius R1=R and R2=1.01R, and length L separated by a homogeneous dielectric with dielectric constant =5.0 as shown in the figure, LR. The inner conductive shell of radius R1 is charged with charges Q1=Q, the outer one (R2) with charges Q2=2Q. Obtain the magnitude of the displacement vector D(r) as a function of r, the distance from the axis of the capacitor. Then find the values of the quantities D(r=R1/2),D(r=(R1+R2)/2) and D(r=2R2). Obtain the magnitude of the electric field E(r), then calculate the values of the quantities E(r=R1/4),E(r=(R1+R2)/2) and E(r=3R2) in terms of 20RLQ units