### Correct Option: A. The induced voltage increases as the magnet approaches the coil. ### Detailed Explanation: **Understanding Faraday's Law of Electromagnetic Induction:** Faraday's law states that a change in magnetic flux through a coil of wire induces an electromotive force (EMF) or voltage in the coil. The law can be mathematically expressed as: \[ \text{EMF} = -\frac{d\Phi_B}{dt} \] Where: - \(\text{EMF}\) is the induced voltage, - \(\Phi_B\) is the magnetic flux, and - \(t\) is time. **What is Magnetic Flux?** Magnetic flux (\(\Phi_B\)) is defined as the product of the magnetic field (\(B\)) and the area (\(A\)) through which the field lines pass, taking into account the angle (\(\theta\)) between the field lines and the normal to the surface: \[ \Phi_B = B \cdot A \cdot \cos(\theta) \] **Effect of Moving a Magnet Towards the Coil:** 1. **Approaching Magnet:** When a magnet is moved towards a coil, the magnetic field strength (\(B\)) experienced by the coil increases. This is because the magnetic field lines from the magnet become denser as the magnet gets closer to the coil. 2. **Change in Magnetic Flux:** As the magnet approaches, the area of the coil remains constant, but the magnetic field strength increases, leading to an increase in magnetic flux (\(\Phi_B\)) through the coil. 3. **Induced Voltage:** According to Faraday's law, since the magnetic flux is increasing over time (\(d\Phi_B/dt > 0\)), the induced voltage (EMF) in the coil will also increase. The negative sign in Faraday's law indicates the direction of the induced current (Lenz's Law), but it does not affect the magnitude of the induced voltage. ### Why Other Options Are Incorrect: - **Option B: The induced voltage decreases as the magnet approaches the coil.** - This is incorrect because the induced voltage is directly related to the rate of change of magnetic flux. As the magnet approaches, the magnetic flux increases, leading to an increase in induced voltage, not a decrease. - **Option C: The induced voltage remains constant regardless of the magnet's position.** - This option is incorrect because the induced voltage is dependent on the change in magnetic flux. If the magnet is stationary, there is no change in flux, and thus no induced voltage. However, as the magnet approaches, the flux changes, and so does the induced voltage. - **Option D: The induced voltage is zero when the magnet is stationary.** - While this statement is true in the context of a stationary magnet, it does not address the scenario of the magnet moving towards the coil. The question specifically asks about the effect of moving the magnet, which leads to an increase in induced voltage. ### Summary of Key Points: - Faraday's law states that a change in magnetic flux induces voltage in a coil. - Moving a magnet towards a coil increases the magnetic flux through the coil. - An increase in magnetic flux results in an increase in induced voltage. - The induced voltage is zero only when there is no change in magnetic flux (e.g., when the magnet is stationary). ### Revision Summary: - **Faraday's Law:** Change in magnetic flux induces voltage. - **Magnetic Flux:** Increases as a magnet approaches a coil. - **Induced Voltage:** Increases with increasing magnetic flux. - **Stationary Magnet:** No induced voltage; movement is key for induction.