AP Free Response Question 2004 C1 E&M

The figure above left shows a hollow, infinite, cylindrical uncharged conducting shell of inner radius r1 and outer radius r2. An infinite line charge density of + is parallel to its axis but off center. An enlarged cross section of the cylindrical shell is shown above on the right.

(a) On the cross section above right

 i. sketch the electric field lines, if any, in each region: I, II, and III

 ii. use + and - signs to indicate any charge induced on the conductor

(b) In the spaces below, rank the electric potentials of points a, b, c, d, and e from highest to lowest (1 = highest potential). If two points are at the same potential, give them the same number.

(c) The shell is replaced by another cylindrical shell that has the same dimensions but is non-conducting and carries a uniform volume charge of +. The infinite line charge, still of charge density +, is located at the center of the shell as shown below.

Using Gauss' Law, calculate the magnitude of the electric field as a function of distance r from the center of the shell for each of the following regions. Express your answers in terms of the given quantities and fundamental constants.

 i. r < r1

 ii. r1 <= r <= r2

 iii. r > r2