### Correct Option: C. The induced voltage will increase. ### Explanation: To understand why the induced voltage in the coil increases when the magnetic field strength increases over time, 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 directly proportional 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), - \(d\Phi_B/dt\) represents the rate of change of magnetic flux. #### Step-by-Step Explanation: 1. **Understanding Magnetic Flux**: - Magnetic flux (\(\Phi_B\)) is defined as the product of the magnetic field strength (B) and the area (A) through which the field lines pass, adjusted for the angle (\(\theta\)) between the magnetic field lines and the normal (perpendicular) to the surface: \[ \Phi_B = B \cdot A \cdot \cos(\theta) \] - In a simple circuit with a coil, if the magnetic field strength (B) increases while the area (A) and angle (\(\theta\)) remain constant, the magnetic flux (\(\Phi_B\)) through the coil also increases. 2. **Rate of Change of Magnetic Flux**: - If the magnetic field strength is increasing over time, the change in magnetic flux (\(d\Phi_B\)) is positive. Therefore, the rate of change of magnetic flux (\(d\Phi_B/dt\)) is also positive. 3. **Induced Voltage**: - According to Faraday's Law, since \(d\Phi_B/dt\) is positive, the induced voltage (emf) will also be positive. 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. - As the magnetic field strength continues to increase, the rate of change of magnetic flux increases, leading to a higher induced voltage. 4. **Conclusion**: - Therefore, as the magnetic field strength increases over time, the induced voltage in the coil will also increase. ### Why Other Options Are Incorrect: - **Option A: The induced voltage will decrease.** - This is incorrect because a decreasing induced voltage would imply that the magnetic flux is decreasing, which contradicts the premise that the magnetic field strength is increasing. - **Option B: The induced voltage will remain constant.** - This option is incorrect because a constant induced voltage would imply that there is no change in magnetic flux. Since the magnetic field strength is increasing, the magnetic flux is also increasing, leading to a change in induced voltage. - **Option D: The induced voltage will become zero.** - This is incorrect because a zero induced voltage would mean that there is no change in magnetic flux. Since the magnetic field strength is increasing, there is a change in magnetic flux, which results in a non-zero induced voltage. ### Summary for Revision: - Faraday's Law states that the induced voltage is proportional to the rate of change of magnetic flux. - An increase in magnetic field strength leads to an increase in magnetic flux through the coil. - The induced voltage will increase as the magnetic field strength increases over time. - Remember that the negative sign in Faraday's Law indicates the direction of the induced current, not the magnitude of the induced voltage.