**Correct Option: 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 when exposed to a changing magnetic field, we need to refer to 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 (\( \Phi_B \))**: - Magnetic flux 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 field lines and the normal to the surface: \[ \Phi_B = B \cdot A \cdot \cos(\theta) \] - A changing magnetic field can occur due to a change in the strength of the magnetic field, the area of the coil, or the angle at which the magnetic field intersects the coil. 2. **Role of the Number of Turns (N)**: - The number of turns in the coil directly multiplies the induced voltage. If you have more turns, each loop of wire experiences the same change in magnetic flux, thus contributing to a higher total induced voltage. - For example, if a coil has 10 turns and the rate of change of magnetic flux is \( 0.1 \, \text{Wb/s} \), the induced voltage would be: \[ \text{emf} = -10 \cdot 0.1 = -1 \, \text{V} \] - If the coil had 20 turns, the induced voltage would double to -2 V, demonstrating the direct relationship between the number of turns and the induced voltage. 3. **Why Other Options Are Incorrect**: - **A. The resistance of the coil**: While resistance affects the current flowing through the coil once the voltage is induced (Ohm's Law: \( V = IR \)), it does not affect the magnitude of the induced voltage itself. The induced voltage is determined by the changing magnetic field and the number of turns. - **C. The material of the coil**: The material can influence the resistance and the efficiency of the coil, but it does not directly affect the induced voltage. The induced voltage is primarily a function of the magnetic flux change and the number of turns. - **D. The temperature of the coil**: Temperature can affect the resistance of the coil and, consequently, the current flowing through it, but it does not influence the induced voltage directly. The induced voltage is determined by the changing magnetic field and the number of turns. ### Common Pitfalls: - Students often confuse the effects of resistance and material properties with the fundamental principles of electromagnetic induction. Remember that while these factors can influence the performance of the coil, they do not change the basic relationship defined by Faraday's Law. - It’s also important to remember that the negative sign in Faraday's Law indicates the direction of the induced voltage (Lenz's Law), which states that the induced emf will always work to oppose the change in magnetic flux. ### Revision Summary: - The primary factor determining the magnitude of induced voltage in a coil is the number of turns in the coil (Option B). - Faraday's Law states that induced voltage is proportional to the rate of change of magnetic flux and the number of turns. - Resistance, material, and temperature affect current and efficiency but not the induced voltage directly. - Always remember the relationship between the number of turns and induced voltage when solving problems related to electromagnetic induction.