The cross-sectional area of an adjustable single loop is reduced from 1.0 m² to 0.25 m² in 0.10 s. What is the average emf that is induced in this coil if it is in a region where B = 2.0 T upward, and the coil's plane is perpendicular to B? A) 0 V B) 15 V C) 12 V D) 21 V E) 18 V

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Quizplus · Accepted Answer

The average emf (ε) induced in a coil when its area changes can be calculated using Faraday's law of electromagnetic induction, which is ε = -ΔΦ/Δt, where ΔΦ is the change in magnetic flux and Δt is the change in time. The magnetic flux (Φ) is given by Φ = B*A*cos(θ), where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the plane of the coil. Since the coil's plane is perpendicular to B, cos(θ) = 1. The change in area (ΔA) is 1.0 - 0.25 = 0.75 m^2. Therefore, ΔΦ = B*ΔA = 2.0 T * 0.75 m^2 = 1.5 Wb. Given Δt = 0.10 s, the average emf is ε = -ΔΦ/Δt = -1.5 Wb / 0.10 s = -15 V. The negative sign indicates the direction of the induced emf, which is not required here, so the magnitude of the emf is 15 V.

The Cross-Sectional Area of an Adjustable Single Loop Is Reduced