A wire loop is placed so that it is in the plane of the paper, as shown below. T

Question

A wire loop is placed so that it is in the plane of the paper, as shown below. The loop is in a region close to a device that can produce a magnetic field through the loop. The graph below shows the strength of the magnetic field produced through the loop as a function of time. Assume that a positive magnetic field is directed out of the page, and a negative magnetic field is directed into the page. On the lower graph, sketch the induced current in the loop as a function of time. Let clockwise be a positive current and counterclockwise be negative current. time

Explanation / Answer

According to Farday's law the B field flux variation (due to B variation this time) induces and emf in the loop. This produces a current that generates a new magnetic field. According to Lenz' law this field is opposite the original one.

Thus when B is out of the page the induced one is in the page and current flows clockwise (positive) and viceversa.

As for current

t<t1 (there are no numbers is the graph!)

B increases linearly, induced current is constant at the B variation slope value dB/dt. Positive (clockwise)

t1<t<t2 B is constant, no emf, induced current is null

t2<t<t3 B increases linearly, induced current is constant at the B variation slope value dB/dt. Positive (clockwise)

t3<t<t4 B is null, no current

t4<t<t5 B decreases linearly, induced current is constant at the B variation slope value dB/dt. negative (counter-clockwise)

t5<t<t6 B is constant, no emf, induced current is null

t6<t<tt B increases linearly, induced current is constant at the B variation slope value dB/dt. Negative (counter-clockwise)

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