Assertion (A): Detent torque is present in permanent magnet stepper motors even when unpowered.

Reason (R): Detent torque arises from the interaction between the rotor magnets and stator teeth.

Which of the following option is correct?

Explanation:

Assertion (A) and Reason (R) Analysis:

Assertion (A): Detent torque is present in permanent magnet stepper motors even when unpowered.

Reason (R): Detent torque arises from the interaction between the rotor magnets and stator teeth.

Stepper motors are widely used in applications where precise positioning and control are required. Among the different types of stepper motors, permanent magnet stepper motors have a unique characteristic called "detent torque." Let us analyze the given statement and reason to determine the correctness of the options provided.

Detent Torque in Permanent Magnet Stepper Motors:

Detent torque is the torque exerted by a stepper motor when it is unpowered. It is a result of the magnetic interaction between the permanent magnets on the rotor and the ferromagnetic material of the stator teeth. This interaction creates a natural alignment between the rotor and the stator teeth, even when no electrical current is supplied to the motor. This alignment creates a resistive force that opposes any external attempt to move the rotor from its natural position, giving rise to detent torque.

Analysis of Assertion (A):

The statement asserts that detent torque is present in permanent magnet stepper motors even when unpowered. This is indeed true because detent torque is a characteristic feature of permanent magnet stepper motors, arising from the magnetic properties of the rotor and stator. It does not depend on the motor being powered or energized.

Analysis of Reason (R):

The reason states that detent torque arises from the interaction between the rotor magnets and stator teeth. This is also true. The rotor of a permanent magnet stepper motor is made of permanent magnets, while the stator has teeth made of ferromagnetic material. The magnetic interaction between these components creates the detent torque that holds the rotor in a specific position even when the motor is unpowered.

Relationship Between Assertion (A) and Reason (R):

Both the assertion and the reason are true, and the reason correctly explains the phenomenon described in the assertion. The detent torque is a direct consequence of the magnetic interaction between the rotor magnets and the stator teeth, as stated in the reason.

Correct Option Analysis:

The correct option is:

Option 4: Both A and R are true, and R explains A.

This option is correct because the assertion is a factual statement about detent torque in permanent magnet stepper motors, and the reason provides a valid and accurate explanation of the underlying cause of detent torque.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Both A and R are true, but R does not explain A.

This option is incorrect because while both the assertion and the reason are true, the reason does indeed explain the assertion. Detent torque arises specifically due to the interaction between the rotor magnets and the stator teeth, as described in the reason.

Option 2: Both A and R are false.

This option is incorrect because both the assertion and the reason are true. Detent torque is a real phenomenon present in permanent magnet stepper motors, and it is caused by the magnetic interaction between the rotor and stator.

Option 3: A is false, but R is true.

This option is incorrect because the assertion is true. Detent torque is indeed present in permanent magnet stepper motors even when unpowered. Additionally, the reason is also true and accurately explains the assertion.

Conclusion:

Understanding the concept of detent torque in permanent magnet stepper motors is essential for applications requiring precise positioning and control. Detent torque is a result of the magnetic interaction between the rotor magnets and the stator teeth, and it is a defining characteristic of permanent magnet stepper motors. The correct option, therefore, is Option 4: Both A and R are true, and R explains A.