**Correct Option: B. The speed of the conductor relative to the magnetic field** ### Detailed Explanation: When a conductor moves through a magnetic field, an electric current can be induced in the conductor due to electromagnetic induction. The magnitude of the induced voltage (also known as electromotive force, or EMF) is primarily determined by several factors, but the most significant one is the speed of the conductor relative to the magnetic field. #### Why Option B is Correct: 1. **Faraday's Law of Electromagnetic Induction**: This law states that the induced EMF in a closed loop is directly proportional to the rate of change of magnetic flux through the loop. Mathematically, it can be expressed as: \[ \text{EMF} = -\frac{d\Phi_B}{dt} \] where \(\Phi_B\) is the magnetic flux. When a conductor moves through a magnetic field, the change in magnetic flux occurs due to the motion of the conductor. 2. **Relative Speed**: The faster the conductor moves through the magnetic field, the greater the change in magnetic flux over time, leading to a higher induced voltage. This is because the induced EMF is proportional to the velocity of the conductor: \[ \text{EMF} = B \cdot L \cdot v \] where: - \(B\) is the magnetic field strength, - \(L\) is the length of the conductor within the magnetic field, - \(v\) is the speed of the conductor relative to the magnetic field. 3. **Practical Example**: If you have a straight wire moving perpendicularly through a uniform magnetic field, increasing the speed of the wire will increase the induced voltage. For instance, if a wire of length 1 meter moves through a magnetic field of strength 0.5 Tesla at a speed of 2 meters per second, the induced EMF can be calculated as: \[ \text{EMF} = 0.5 \, \text{T} \cdot 1 \, \text{m} \cdot 2 \, \text{m/s} = 1 \, \text{V} \] ### Why the Other Options are Incorrect: - **Option A: The temperature of the conductor**: While temperature can affect the resistance of the conductor and thus the overall current flowing through it, it does not directly influence the magnitude of the induced voltage. The induced voltage is primarily a function of motion through the magnetic field, not the thermal state of the conductor. - **Option C: The length of the conductor**: Although the length of the conductor does play a role in determining the induced voltage (as seen in the formula \( \text{EMF} = B \cdot L \cdot v \)), it is not the primary factor. The length is a multiplicative factor, meaning that for a given speed and magnetic field strength, a longer conductor will indeed produce a higher voltage, but it does not change the fundamental relationship that the speed of the conductor is the most critical factor. - **Option D: The strength of the magnetic field only**: Similar to the length of the conductor, the strength of the magnetic field is also a factor in the induced voltage. However, it is not the only factor, and it does not account for the effect of the conductor's speed. The induced voltage depends on both the magnetic field strength and the speed of the conductor. ### Summary of Key Points: - The induced voltage in a conductor moving through a magnetic field is primarily determined by the speed of the conductor relative to the magnetic field. - Faraday's Law states that the induced EMF is proportional to the rate of change of magnetic flux, which is influenced by the speed of the conductor. - The formula for induced EMF includes the magnetic field strength, length of the conductor, and speed, highlighting that speed is a critical factor. - Temperature and the strength of the magnetic field are not the primary determinants of induced voltage, although they do play a role in the overall system. This understanding is crucial for solving problems related to electromagnetic induction in physics.