The area of a rectangular loop of wire is 3.6 × 10^-3 m². The loop is placed in a magnetic field that changes from 0.20 T to 1.4 T in 1.6 s. The plane of the loop is perpendicular to the direction of the magnetic field. What is the magnitude of the induced emf in that loop? A) 2.8 × 10^-3 V B) 2.7 × 10^-3 V C) 0 V D) 1.8 × 10^-3 V E) 3.0 × 10^-3 V

Question

Quizplus · Accepted Answer

The induced emf can be found using the equation Emf = -N(dΦ/dt), where N is the number of turns in the loop, Φ is the magnetic flux through the loop, and t is time. We know that the magnetic field changes from 0.20 T to 1.4 T in 1.6 s, so the average rate of change of the magnetic field is (1.4 T - 0.20 T)/1.6 s = 0.75 T/s. Since the magnetic field is perpendicular to the loop, the magnetic flux through the loop is given by Φ = BA, where B is the magnetic field and A is the area of the loop. Substituting the given values, we have Φ = (1.4 T)(3.6 × 10^-3 m^2) = 5.04 × 10^-3 Wb. Therefore, the induced emf is Emf = -N(dΦ/dt) = -(1)(0.75 T/s) = -0.75 V. However, the question asks for the magnitude of the emf, so we take the absolute value to get 0.75 V, which is equivalent to 2.7 × 10^-3 ¥. Therefore, the best choice is B.

The Area of a Rectangular Loop of Wire Is 3