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Problem 20 Medium Difficulty

A circular coil enclosing an area of 100 $\mathrm{cm}^{2}$ is made of 200 turns of copper wire. The wire making up the coil has resistance of 5.0$\Omega$ , and the ends of the wire are connected to form a closed circuit. Initially, a 1.1-T uniform magnetic field points perpendicularly upward through the plane of the coil. The direction of the field then reverses so that the final magnetic field has a magnitude of 1.1 T and points downward through the coil. If the time required for the field to reverse directions is 0.10 s, what is the average current in the coil during that time?

Answer

8.8 A

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Video Transcript

we're told that we have a coil that has a number of turns of 200 so in is equal to 200 with an area of 100 square centimeters or 1000.1 square meters. So this coil has a magnetic field, be of 1.1 Tesla's and resistance in the coils wires of five homes. And we're told that in a time of 0.1 seconds, the magnetic field is completely reversed. So that way the magnetic field so has the same magnitude 1.1 Tesla, but is now in the office direction or asked to find the average current in the coil during that time. Well, the current in the coil I during that time is going to be equal to the, uh, induced e m f from the change in the magnetic flux divided by the resistance are Well, we don't we know are, But we don't know the induced Ian meth. So we need to find the induced in death. Well, the magnitude of the induced you meth is equal to the magnitude of the change in flux. Divided by the change in time delta t we know Delta t so. Therefore we need to find the magnitude of the change in flux. So the change in flux is the final flux, minus the initial flux. So here, um uh, FYI is the initial flux initially the normal line and magnetic field liner in the same direction And fi f is the final flux Where the normal line of the magnetic field liner in opposite directions. So initially, the normal line in the magnetic field liner in the same direction. So the initial angle will call this, uh, they die is going to be equal to zero degrees and then in the final, the normal line in the magnetic field line or in opposite directions, so the final angle will call it Data s is going to be equal to 180 degrees. Okay, so now, um, the induced CMF expression we can write the explicit forms of, uh, the final flux in the initial flux. So we want the magnitude of the final flux, which is the number of terms times the area times the magnetic feel times the co sign of the final angle. They'd ask, minus the number of turns times the area times the magnetic field which is the exact same as the final case in the initial case. But this time the angle changes. So this is co sign of the initial angled. They die. Now, this relationship is gonna give us a negative number. But since we care about magnitude, the negative number doesn't matter. And then, of course, this is still divided by Delta t, which were told this 0.1 seconds. So clinging those values into this expression, we find that the induce CMF is 44 and the units here are volts. So the induce CMF is 44 volts. Now that we know the induced Ian meth, we can go ahead and find the current. Since the current I is equal to the magnitude of the induced you meth, which we just found to be 44 volts divided by the resistance, which we were told was five owns plugging those values. In this expression, we get eight 0.8 and the units here car amperes, we can go ahead and box set in as their solution to this question.

University of Kansas
Top Physics 102 Electricity and Magnetism Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

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Aspen F.

University of Sheffield

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