Some practice with an infinite line charge. (a) What is the electric field on an infinite line charge that has a constant charger per unit length of X? (b) What is the electrostatic potential in this case? Is it possible to make the potential vanish at infinity? (c) Consider an infinite conducting cylinder of radius a that is grounded. Suppose there is an infinite line charge with a constant charge per unity length that is located inside the cylinder, such that it is parallel to the cylinder, but displaced from the central axis by an amount b, with b < a. Determine the electrostatic potential everywhere inside the cylinder. I suggest using the method of images, by placing another line charge outside

A spherical capacitor contains a charge q when connected to a potential difference V. Its plates are separated by vacuum and the outer radius of the inner shell is r.  What is the inner radius of the outer shell?  Answer in terms of k instead of 1/4πϵ01/4πϵ0.

A capacitor consists of 3 spherical shells with radiuses r, 2r and 4r. The first and third shells are connected to earth but the second one has charge 5Q, calculate the capacity and the charge on the third ( outer) shell.