Which component closes the circuit to start the motor when a magnetic field is present?

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Detecting a magnetic field and turning that into a switch closed to run the motor is what this item is about. A Hall effect sensor is designed to respond directly to magnetic fields. Its Hall element sits in a current path, and when a magnetic field passes perpendicular to that path, it generates a Hall voltage. The sensor’s circuitry reads this voltage and, when the field is present (and reaches the switching threshold), it changes its output to a closed state, allowing current to flow and the motor to start.

The other options don’t rely on magnetic field detection to close a circuit. A photoelectric sensor uses light to detect objects or beams, a capacitive sensor detects changes in capacitance caused by nearby materials, and a general proximity sensor detects nearby objects through various methods that aren’t specifically about sensing a magnetic field. Since the requirement is closing the circuit in response to magnetism, the Hall effect sensor is the appropriate choice.