A short cylinder, of radius a and length L, carries a ``frozen-in'' uniform 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.]