Planar motor, positioning apparatus, exposure apparatus, and device manufacturing method

A planar motor comprising:

• a stator in which a plurality of convex portions each containing a magnetic material are arranged;
• and
• a movable element which faces the stator,
• the movable element including a plurality of coils and a plurality of teeth,
• wherein the movable element moves in at least a first direction using a magnetic flux generated by controlling electric currents flowing through the plurality of coils, and
• as the teeth and the convex portions move relative to each other upon the movement of the movable element in the first direction, a spatial derivative of a magnetic flux running area, as an area of a region in which the magnetic flux runs through a portion in which the plurality of convex portions overlap the teeth, gradually increases and decreases.

A planar motor comprising:

• a stator including a recessed portion and a plurality of convex portions each containing a magnetic material;
• and
• a movable element which faces the stator,
• the movable element including a plurality of coils,
• wherein the movable element moves by controlling electric currents flowing through the plurality of coils,
• each of the convex portions is a quadrangle in which four corners are adjacent to each other and four sides are adjacent to the recessed portion, and
• the movable element moves in a direction along at least one of axes running on diagonals of each of the convex portions.

A planar motor comprising:

• a stator in which a plurality of convex portions each containing a magnetic material are arranged;
• and
• a movable element which faces the stator,
• the movable element including a plurality of coils,
• wherein the movable element moves by controlling electric currents flowing through the plurality of coils, and
• each of the convex portions has a shape including four corners, and the convex portions are arranged such that an interval between an edge of a given convex portion and an edge of a convex portion closest to the given convex portion becomes less than half an interval between the center of the given convex portion and the center of the convex portion closest to the given convex portion.

A planar motor comprising:

• a stator in which a plurality of convex portions each containing a magnetic material are arranged;
• and
• a movable element which faces the stator,
• the movable element including a plurality of coils,
• wherein the movable element moves in at least a first direction by controlling electric currents flowing through the plurality of coils, and
• each of the convex portions has a shape including eight corners, and the convex portions are arranged such that an interval between an edge of a given convex portion and an edge of a convex portion closest to the given convex portion becomes less than half an interval between the center of the given convex portion and the center of the convex portion closest to the given convex portion.