[ ] Because the slope of the graph at t = 17.5 s has the opposite sign of the sl

Question

[ ] Because the slope of the graph at t = 17.5 s has the opposite sign of the slope of the graph at t = 40 s, the direction of the induced current at t = 17.5 s is in the opposite direction of the induced current at t = 40 s.
[ ] Because the flux is the same at both times, the magnitude of the induced current is the same at both times.
[ ]Because 17.5 seconds is a shorter time interval than 40 seconds, and the induced emf equation has the time interval in the denominator, the magnitude of the induced current is larger at t = 17.5 s than at t = 40 s.
[ ]Because the magnitude of the slope of the graph is four times larger at t = 17.5 s than it is at t = 40 s, the magnitude of the induced current is four times larger at t = 17.5 s than it is at t = 40 s.
[ ]Because the flux is positive at both times, the direction of the induced current is the same at both times.

The graph below shows the magnetic flux through a conducting loop as a function of time. The units of flux are webers, which are equivalent to tesla meters2. The flux in the loop changes because the magnetic field passing through the loop changes. The loop itself is stationary. Assume that the field is uniform and the direction of the field is perpendicular to the plane of the loop. The loop has a resistance of 0.300 ?, an area of 4.00 m2, and consists of a single turn. Note that you should be able to do this problem without a calculator. (c) From the graph, we can see that the flux passing through the loop is 3.0 webers at both t = 17.5s and t = 40s. Select the two statements below that correctly describe how the induced current in the loop at t = 17.5 seconds compares to the induced current in the loop at t = 40 s. [ ] Because the slope of the graph at t = 17.5 s has the opposite sign of the slope of the graph at t = 40 s, the direction of the induced current at t = 17.5 s is in the opposite direction of the induced current at t = 40 s. [ ] Because the flux is the same at both times, the magnitude of the induced current is the same at both times. [ ]Because 17.5 seconds is a shorter time interval than 40 seconds, and the induced emf equation has the time interval in the denominator, the magnitude of the induced current is larger at t = 17.5 s than at t = 40 s. [ ]Because the magnitude of the slope of the graph is four times larger at t = 17.5 s than it is at t = 40 s, the magnitude of the induced current is four times larger at t = 17.5 s than it is at t = 40 s. [ ]Because the flux is positive at both times, the direction of the induced current is the same at both times.

Explanation / Answer

Because the slope of the graph at t = 17.5 s has the opposite sign of the slope of the graph at t = 40 s, the direction of the induced current at t = 17.5 s is in the opposite direction of the induced current at t = 40 s.

Because the magnitude of the slope of the graph is four times larger at t = 17.5 s than it is at t = 40 s, the magnitude of the induced current is four times larger at t = 17.5 s than it is at t = 40 s.

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