This　article　presents　an　exact　analytical　method　for　active　magnetic　bearings　to　obtain　the　magnetic　field　distribution　with　rotor　eccentricity.　Based　on　the　subdomain　method　and　the　perturbation　method,　the　active　magnetic　bearing　is　divided　into　two　regions:　the　air　gap　and　stator　slots.　Meanwhile,　the　zeroth-order　and　first-order　equations　in　the　polar　coordinate　are　obtained　and　solved　by　the　method　of　separation　of　variables,　respectively.　The　magnetic　field　distribution　is　obtained　by　superimposing　the　first-order　solution　into　the　zeroth-order　solution　according　to　the　perturbation　method.　The　proposed　analytical　method　has　provided　an　effective　way　to　study　the　magnetic　bearing　and　other　electromagnetic　actuators.　By　using　the　Maxwell　stress　tensor　theory,　the　unbalanced　magnetic　force　is　calculated　to　obtain　the　displacement　stiffness　and　current　stiffness.　Finally,　the　consequences　of　magnetic　field　distribution　and　the　unbalanced　magnetic　force　are　compared　with　those　by　the　finite-element　method.　The　result　validates　the　correctness　of　the　analytical　method.　©　1965-2012　IEEE.