Time-varying magnetic fields of magnets in booster accelerators induce substantial eddy currents in the vacuum chambers. The eddy currents in turn act to produce various multipole fields that act on the beam. These fields must be taken into account when doing a lattice design. In the APS booster, the relatively long dipole magnets (3 meters) are linearly ramped to accelerate the injected 325 MeV beam to 7 GeV. Substantial dipole and sextupole fields are generated in the elliptical vacuum chamber from the induced eddy currents. In this note, formulas for the induced dipole and sextupole fields are derived for elliptical and rectangular vacuum chambers for a time-varying dipole field. A discussion is given on how to generalize this derivation method to include eddy-current-induced multipole fields from higher multipole magnets (quadrupole, sextupole, etc.). Finally, transient effects are considered.