Dust polarization in millimeter (and centimeter) has been mapped in disks around an increasing number of young stellar objects. It is usually thought to come from emission by magnetically aligned (non-spherical) grains, but can also be produced by dust scattering. We present a semi-analytic theory of disk polarization that includes both the direction emission and scattering, with an emphasis on their relative importance and how they are affected by the disk inclination. For face-on disks, both emission and scattering tend to produce polarization in the radial direction, making them difficult to distinguish, although the scattering-induced polarization can switch to the azimuthal direction if the incident radiation is beamed strongly enough in the radial direction in the disk plane. Disk inclination affects the polarizations from emission and scattering differently, especially on the major axis where, in the edge-on limit, the former vanishes while the latter reaches a polarization fraction as large as 1/3. The polarizations from the two competing mechanisms tend to cancel each other on the major axis, producing two low polarization holes (one on each side of the center) under certain conditions. We find tantalizing evidence for at least one such hole in NGC1333 IRAS4A1, whose polarization observed at 8 mm on the 100 AU scale is indicative of a pattern dominated by scattering close to the center and by direction emission in the outer region. If true, it would imply not only that a magnetic field exists on the disk scale, but that it is strong enough to align large, possibly mm-sized, grains.
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