### Correct Option: D. The induced voltage increases. ### Detailed Explanation: To understand why the correct answer is D, we need to delve into Faraday's Law of Electromagnetic Induction, which states that the induced electromotive force (emf) in any closed circuit is equal to the rate of change of the magnetic flux through the circuit. The formula for Faraday's Law can be expressed as: \[ \text{emf} = -\frac{d\Phi_B}{dt} \] Where: - \(\text{emf}\) is the induced voltage (in volts), - \(\Phi_B\) is the magnetic flux (in webers), - \(t\) is time (in seconds), - \(d\Phi_B/dt\) is the rate of change of magnetic flux. #### 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) and the area (A) of the loop perpendicular to the magnetic field. Mathematically, it can be expressed as: \[ \Phi_B = B \cdot A \cdot \cos(\theta) \] where \(\theta\) is the angle between the magnetic field lines and the normal (perpendicular) to the surface of the loop. 2. **Decreasing Magnetic Field**: - In this scenario, we are told that the magnetic field passing through the loop is decreasing at a constant rate. This means that the value of \(B\) is getting smaller over time. 3. **Rate of Change of Magnetic Flux**: - As the magnetic field decreases, the magnetic flux (\(\Phi_B\)) through the loop also decreases. Since the area \(A\) and the angle \(\theta\) remain constant, the change in flux is directly related to the change in the magnetic field strength: \[ \frac{d\Phi_B}{dt} = A \cdot \frac{dB}{dt} \cdot \cos(\theta) \] Here, \(\frac{dB}{dt}\) is negative because the magnetic field is decreasing. 4. **Induced Voltage**: - According to Faraday's Law, since \(\frac{d\Phi_B}{dt}\) is negative (the flux is decreasing), the induced voltage (\(\text{emf}\)) will be positive (the negative sign in the formula indicates the direction of the induced current, not the magnitude). Therefore, the induced voltage increases as the magnetic field decreases. 5. **Direction of Induced Voltage**: - The induced voltage will act in such a way as to oppose the change in magnetic flux (Lenz's Law). This means that if the magnetic field is decreasing, the induced current will flow in a direction that tries to maintain the magnetic field within the loop. ### Why Other Options Are Incorrect: - **Option A: The induced voltage increases in the opposite direction.** - This option is misleading. While the induced voltage does oppose the change in magnetic flux (Lenz's Law), it does not mean that the voltage itself increases in the opposite direction. The magnitude of the induced voltage increases, but its direction is determined by the nature of the change in flux. - **Option B: The induced voltage remains constant.** - This is incorrect because the induced voltage is directly related to the rate of change of the magnetic field. Since the magnetic field is decreasing, the induced voltage cannot remain constant; it must change as the magnetic field changes. - **Option C: The induced voltage decreases.** - This option contradicts Faraday's Law. If the magnetic field is decreasing, the induced voltage must increase in response to that change, not decrease. ### Summary for Revision: - **Faraday's Law** states that induced voltage is proportional to the rate of change of magnetic flux. - A **decreasing magnetic field** leads to a **decrease in magnetic flux**, resulting in an **increase in induced voltage**. - The direction of the induced voltage opposes the change in magnetic flux (Lenz's Law). - Always remember that the induced voltage responds to changes in the magnetic field, not to its absolute value.