Problem 4.11 A short cylinder, of radius a and length L, carries a "frozen-in" uni-form polarization P, parallel to its axis. Find the bound charge, and sketch the electric field

(i) for L >a, (ii) for L«a, and (iii) for L a. [This is known as a bar electret; it is the electrical analog to a bar magnet. In practice, only very special materials-barium titanate is the most "familiar" example-will hold a permanent electric polarization. That's why you can't buy electrets at the toy store.]