Induced currents by magnetic fields A magnetic field passes through a stationary
ID: 1667527 • Letter: I
Question
Induced currents by magnetic fieldsA magnetic field passes through a stationary wire loop, and its magnitude changes in time according to the graph in the drawing. The direction of the field remains constant, however. There are three equal time intervals indicated in the graph: 0 - 3.0 s, 3.0 - 6.0 s, and 6.0 - 9.0 s.
(a) Is the induced emf equal to zero during any of the intervals?
There is no time interval in which the induced emf is zero.
The induced emf is zero during the 3.0 - 6.0 s interval.
The induced emf is zero during the 6.0 - 9.0 s interval.
The induced emf is zero during the 0 - 3.0 s interval.
(b) During which interval is the magnitude of the induced emf the largest?
0 - 3.0 s
6.0 - 9.0 s
3.0 - 6.0 s
(c) If the direction of the current induced during the first interval is clockwise, what is the direction during the third interval?
clockwise
counterclockwise
The loop consists of 50 turns of wire and has an area of 0.17 m2. The magnetic field is oriented parallel to the normal to the loop. For purposes of this problem, this means that ? = 0° in Equation 22.2.
= BA cos(?)
Equation 22.2
(d) For the interval from 0 - 3.0 s, determine the induced emf .
Sign Number Unit = 4---Select----
Explanation / Answer
a. The induced emf is zero during the second interval, 3.0 –6.0 s. According to Faraday’s law of electromagnetic induction, Equation 22.3, aninduced emf arises only when the magnetic flux changes. During this interval, the magneticfield, the area of the loop, and the orientation of the field relative to the loop are constant.Thus, the magnetic flux does not change, so there is no induced emf. b. An emf is induced during the first and third intervals, becausethe magnetic field is changing in time. The time interval is the same (3.0 s) for the twocases. However, the magnitude of the field changes more during the first interval.Therefore, the magnetic flux is changing at a greater rate in that interval, which means that themagnitude of the induced emf is greatest during the first interval. c. During the first interval the magnetic field in increasing withtime. During the third interval, the field is decreasing with time. As a result, theinduced emfs will have opposite polarities during these intervals. If the direction of the inducedcurrent is clockwise during the first interval, it will be counterclockwise during the thirdinterval.