Final answer:
The average electromotive force (emf) induced in the coil when it is rotated from an angle of 35 degrees to perpendicular in a magnetic field of 1.21 T is found to be 79.2 V. This is calculated using Faraday's Law of Induction.
Step-by-step explanation:
To calculate the average electromotive force (emf) induced in the coil, we can use Faraday's Law of Induction, which is given by Ε = -N ΔΦ/Δt, where Ε is the emf, N is the number of turns, and ΔΦ/Δt is the rate of change of magnetic flux. The change in flux (ΔΦ) is equal to the change in the magnetic field (ΔB) times the area of the coil (A) times the cosine of the angle (θ) between the field and normal to the coil plane. In this scenario, we have Δθ from 35° to 90°, therefore going from cos(35°) to cos(90°), which is 0.
The area A of the rectangle is length times width, so A = 0.25 m × 0.40 m. Hence ΔΦ = B × A × (Δcos(θ)) = 1.21 T × 0.25 m × 0.40 m × (cos(35°) - cos(90°)). Because cos(90°) equals to 0, this simplifies to ΔΦ = 1.21 T × 0.25 m × 0.40 m × cos(35°).
Plugging in the values, we get ΔΦ = 1.21 T × 0.25 m × 0.40 m × 0.819 = 0.0792 Tm². Since the coil has 75 turns and time Δt = 0.075 s, the average emf induced is Ε = -75 turns × 0.0792 Tm² / 0.075 s = -79.2 V/s. The negative sign indicates the direction of the induced emf, which is a reduction according to Lenz's Law, but we mostly are concerned with the magnitude here, which is 79.2 V.