A metal loop has an area of 0.450 m² and is placed flat on the ground.There is a uniform magnetic field pointing directly out of the ground.This magnetic field initially has a value of 0.728 T but this decreases to 0.150 T uniformly during a period of 0.238 s.Find the voltage induced in the loop during this time. A)zero B)0.26 V C)1.1 V D)1.7 V E)2.4 V

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Quizplus · Accepted Answer

The voltage induced in the loop can be found using the equation: EMF = -N*d(phi)/dt where N is the number of turns in the loop and d(phi)/dt is the rate of change of magnetic flux through the loop. Since the magnetic field is uniform, the rate of change of magnetic flux through the loop is simply: d(phi)/dt = B*A*cos(theta)/dt where B is the magnetic field, A is the area of the loop, and theta is the angle between the magnetic field and the normal to the loop (which is 90 degrees in this case). Plugging in the given values, we get: d(phi)/dt = (0.728 T)(0.450 m^2)/0.238 s = 1.376 V Note that we converted the units of area from m² to m^2. So the EMF induced in the loop is: EMF = -N*d(phi)/dt = -(1)(1.376 V) = -1.376 V Since the loop is a closed circuit, the induced current will flow in a direction such that it creates a magnetic field that opposes the change in the external magnetic field. This means that the induced voltage should be positive, so we take the absolute value of the EMF to get: |EMF| = 1.376 V, which is closest to choice C (1.1 V).

A Metal Loop Has an Area of 0