A capacitor consists of two conducting, coaxial, cylindrical shells of radius a and b, respectively, and length L >> b. The space betweenthe cylinders is filled with oil that has a dielectric constantx. Initially both cylinders are uncharged, butthen a battery is used to charge the capacitor, leaving a charge +Qon the inner cylinder and -Q on the outer cylinder, as shown above. Let r be the radial distance from the axis of thecapacitor.

a. Using Gauss's law, determine the electric field midway along the length of thecylinder for the following values of r, in terms of thegiven quantities and fundamental constants. Assume end effects are negligible.

i. a < r
ii. b < r<< L

b. Determine thefollowing in terms of the given quantities and fundamentalconstants.

i. The potentialdifference across the capacitor

ii. Thecapacitance of this capacitor