### Correct Option: B. The induced voltage remains constant as long as the loop is moving at a constant speed. #### Detailed Explanation: To understand why option B is correct, we need to delve into the principles of electromagnetic induction, specifically Faraday's Law of Electromagnetic Induction. This law states that the induced electromotive force (emf) in a closed loop is directly proportional to the rate of change of magnetic flux through the loop. 1. **Understanding Magnetic Flux**: - Magnetic flux (\( \Phi_B \)) is defined as the product of the magnetic field strength (\( B \)) and the area (\( A \)) of the loop that is perpendicular to the magnetic field. Mathematically, it can be expressed as: \[ \Phi_B = B \cdot A \cdot \cos(\theta) \] - Here, \( \theta \) is the angle between the magnetic field lines and the normal (perpendicular) to the surface of the loop. 2. **Induced Voltage**: - According to Faraday's Law, the induced voltage (\( \mathcal{E} \)) in the loop is given by: \[ \mathcal{E} = -\frac{d\Phi_B}{dt} \] - This means that the induced voltage is related to how quickly the magnetic flux through the loop is changing. 3. **Loop Entering the Magnetic Field**: - As the loop begins to enter the magnetic field, the area of the loop that is within the magnetic field increases. If the loop is moving at a constant speed, the rate at which the area enters the magnetic field remains constant, leading to a constant rate of change of magnetic flux. - Therefore, the induced voltage will be constant while the loop is moving at a constant speed into the magnetic field. 4. **Loop Fully Within the Magnetic Field**: - Once the loop is fully within the magnetic field, the area of the loop that is exposed to the magnetic field does not change anymore. As a result, the magnetic flux through the loop becomes constant, and thus the induced voltage becomes zero. However, this situation is not covered by option B, which only states that the induced voltage remains constant while the loop is moving. 5. **Loop Exiting the Magnetic Field**: - As the loop exits the magnetic field, the area of the loop that is within the magnetic field decreases, which again leads to a change in magnetic flux. If the loop is moving at a constant speed, the induced voltage will again be constant but in the opposite direction (due to Lenz's Law). #### Why Other Options Are Incorrect: - **Option A**: "The induced voltage increases indefinitely as the loop enters the field." - This is incorrect because the induced voltage does not increase indefinitely. It remains constant as long as the loop is moving at a constant speed into the magnetic field. The voltage only changes when the rate of change of magnetic flux changes. - **Option C**: "The induced voltage is zero when the loop is fully within the magnetic field." - While this statement is true, it does not address the question about the effect of motion into the magnetic field. The question specifically asks about the induced voltage while the loop is moving, not when it is fully within the field. - **Option D**: "The induced voltage decreases as the loop exits the magnetic field." - This option is misleading. While it is true that the induced voltage will change direction as the loop exits the magnetic field, it does not decrease in the sense of becoming less than zero; rather, it becomes a constant negative value as the loop continues to exit. ### Summary for Revision: - The induced voltage in a loop moving into a magnetic field at constant speed remains constant due to a constant rate of change of magnetic flux. - Faraday's Law states that induced voltage is proportional to the rate of change of magnetic flux. - The induced voltage becomes zero when the loop is fully within the magnetic field, but this is not the focus of the question. - Understanding the relationship between motion, magnetic flux, and induced voltage is crucial for solving problems related to electromagnetic induction.