A magnetic field can exert a magnetic force on a wire if the wire is carrying a current. (F=BIL). This is the basis for all electric motors.
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Here is a home-made toy DC motor: It works despite having no commutator. How come?
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2 segments of the wire must be experiencing magnetic forces in opposite directions, in order for the heart to spin. Can you identify the segments?
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This motor is rotated by one single torque (instead of a couple). Can you figure out how it works?