Sure, let's down the problem and solve it step by step. --- ### **Step 1: Calculate the Change in Magnetic Flux** - **Given:** - Number of turns, \( N = 15 \) - Area, \( A = .40 \, \text{m}^2 \) - Initial orientation: Plane of coil parallel to magnetic field (\( \theta_1 = ^\circ \)), so flux \( \Phi_1 = B \cdot A \cdot \cos(^\circ) = \) - Final orientation: Plane of coil perpendicular (\( \theta_2 = 90^\circ \)), so flux \( \Phi_2 = B \cdot A \cdot \cos(90^\circ) = B \cdot A \) - Magnetic field, \( B = .25 \, \text{T} \) - **Change in flux:** \[ \Delta \Phi = \Phi_2 - \Phi_1 = (B \cdot A) - = (.25 \times .40) = .10 \, \text{Wb (per turn)} \] For 15 turns: \( \Delta \Phi_{total} = N \times \Delta \Phi = 15 \times .10 = 1.5 \, \text{Wb} \) **Explanation:** The change in magnetic flux (\( \Delta \Phi \)) is found by considering the difference in flux through the coil as it rotates from being parallel to perpendicular to the field. --- ### **Step 2: Calculate the Induced EMF Using Faraday's Law** - **Time taken, \( \Delta t = .080 \, \text{s} \)** - **Faraday’s Law:** \[ \text{Average induced emf} = \left| \frac{\Delta \Phi_{total}}{\Delta t} \right| \] \[ = \left| \frac{1.5}{.080} \right| = 18.75 \, \text{V} \] **Explanation:** Faraday’s Law states that the induced emf is equal to the rate of change of magnetic flux. We use the total flux change for all turns and divide by the time interval. --- ## **Final Answer** **The magnitude of the average induced emf in the coil is \( \boxed{18.75 \, \text{V}} \).**