The correct option is **B. The number of turns in the coil**. ### Detailed Explanation To understand why the number of turns in the coil is the primary factor that determines the magnitude of the induced voltage, 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 equal to the rate of change of the magnetic flux through the circuit. The formula for Faraday's Law can be expressed as: \[ \text{emf} = -N \frac{d\Phi_B}{dt} \] Where: - \(\text{emf}\) is the induced voltage, - \(N\) is the number of turns in the coil, - \(\Phi_B\) is the magnetic flux, and - \(\frac{d\Phi_B}{dt}\) is the rate of change of magnetic flux. #### Step-by-Step Breakdown: 1. **Understanding 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, adjusted for the angle (\(\theta\)) between the magnetic field and the normal to the surface: \[ \Phi_B = B \cdot A \cdot \cos(\theta) \] 2. **Rate of Change of Magnetic Flux**: - When the magnetic field changes (either in strength, direction, or area), the magnetic flux through the coil changes. The rate of this change (\(\frac{d\Phi_B}{dt}\)) is crucial for inducing voltage. 3. **Role of the Number of Turns**: - The term \(N\) in Faraday's Law indicates that the induced voltage is directly proportional to the number of turns in the coil. More turns mean that the same change in magnetic flux will induce a greater total voltage because each loop of wire experiences the same change in flux. 4. **Induced Voltage Calculation**: - For example, if a coil has 10 turns and the rate of change of magnetic flux is 0.1 Weber per second, the induced voltage would be: \[ \text{emf} = -10 \cdot 0.1 = -1 \text{ V} \] If the coil had 20 turns, the induced voltage would be: \[ \text{emf} = -20 \cdot 0.1 = -2 \text{ V} \] This illustrates how increasing the number of turns increases the induced voltage. ### Why the Other Options Are Incorrect: - **A. The temperature of the coil**: - While temperature can affect the resistance of the wire and thus the efficiency of the circuit, it does not directly influence the induced voltage according to Faraday's Law. The induced voltage is fundamentally linked to the magnetic flux change and the number of turns. - **C. The length of the wire used**: - The length of the wire does not directly affect the induced voltage. It may influence the resistance of the coil, but the induced voltage is determined by the number of turns and the rate of change of magnetic flux, not the length of the wire. - **D. The resistance of the circuit**: - Resistance affects the current that flows in the circuit once the voltage is induced, but it does not determine the magnitude of the induced voltage itself. The induced voltage is a function of the magnetic field change and the number of turns. ### Common Pitfalls: - Students often confuse the effects of resistance and the number of turns. While resistance affects how much current flows for a given voltage, it does not influence the voltage induced by changing magnetic fields. - Another common mistake is to overlook the importance of the rate of change of magnetic flux. Students should remember that both the number of turns and the rate of change of flux are critical for determining induced voltage. ### Revision Summary: - The induced voltage in a coil is primarily determined by the number of turns in the coil. - Faraday's Law states that induced voltage is proportional to the rate of change of magnetic flux and the number of turns. - Temperature, wire length, and resistance do not directly affect the induced voltage. - Always consider both the number of turns and the rate of change of magnetic flux when analyzing induced voltage scenarios.