### Correct Option: B. It is directly proportional to the rate of change of magnetic flux. #### Detailed Explanation: To understand why option B is correct, we need to delve into Faraday's Law of Electromagnetic Induction. This law states that the induced electromotive force (emf) in any closed circuit is directly proportional to the rate of change of magnetic flux through the circuit. The mathematical expression for Faraday's Law is given by: \[ \text{emf} = -\frac{d\Phi_B}{dt} \] Where: - \(\text{emf}\) is the induced voltage (in volts), - \(\Phi_B\) is the magnetic flux (in webers), - \(\frac{d\Phi_B}{dt}\) is the rate of change of magnetic flux (in webers per second). **Step-by-Step Explanation:** 1. **Understanding Magnetic Flux**: Magnetic flux (\(\Phi_B\)) through a loop is defined as the product of the magnetic field strength (B), the area of the loop (A), and the cosine of the angle (\(\theta\)) between the magnetic field lines and the normal (perpendicular) to the surface of the loop: \[ \Phi_B = B \cdot A \cdot \cos(\theta) \] 2. **Rate of Change of Magnetic Flux**: When the magnetic field strength, the area of the loop, or the angle changes, the magnetic flux through the loop changes. If this change occurs at a constant rate, it means that \(\frac{d\Phi_B}{dt}\) is a constant value. 3. **Induced Voltage**: According to Faraday's Law, the induced voltage (emf) is directly proportional to this rate of change of magnetic flux. Therefore, if the magnetic flux changes at a constant rate, the induced voltage will also be constant and directly proportional to that rate. 4. **Negative Sign**: The negative sign in Faraday's Law indicates the direction of the induced emf (Lenz's Law), which states that the induced current will flow in a direction that opposes the change in magnetic flux. However, for the purpose of this question, we focus on the magnitude of the induced voltage, which is directly proportional to the rate of change. #### Why Other Options Are Incorrect: - **Option A: It remains constant throughout the change.** - This option is incorrect because the induced voltage does not remain constant if the magnetic flux is changing. Instead, it is the rate of change of the magnetic flux that determines the induced voltage. If the flux changes, the induced voltage will also change accordingly. - **Option C: It is inversely proportional to the area of the loop.** - This option is misleading. While the area of the loop does affect the magnetic flux (\(\Phi_B = B \cdot A \cdot \cos(\theta)\)), the induced voltage is not inversely proportional to the area. In fact, for a given magnetic field and angle, a larger area would result in a greater magnetic flux and thus a greater induced voltage if the flux changes. - **Option D: It depends solely on the strength of the magnetic field.** - This option is also incorrect. While the strength of the magnetic field (B) does play a role in determining the magnetic flux, the induced voltage depends on the rate of change of the magnetic flux, which is influenced by both the magnetic field strength and the area of the loop. Therefore, it cannot depend solely on the strength of the magnetic field. ### Revision Summary: - Faraday's Law states that induced voltage is proportional to the rate of change of magnetic flux. - The formula for induced voltage is \(\text{emf} = -\frac{d\Phi_B}{dt}\). - Induced voltage changes with changing magnetic flux, not remaining constant. - The area of the loop and the magnetic field strength both influence the magnetic flux, but the induced voltage is specifically related to how quickly that flux changes.