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A long solenoid of radius $r=2.00 \mathrm{cm}$ is wound with $3.50 \times 10^{3}$ turns/m and carries a current that changes at the rate of 28.5 $\mathrm{A} / \mathrm{s}$ as in Figure $\mathrm{P} 20.60 .$ What is the magnitude of the emf induced in the square conducting loop surrounding the center of the solenoid?

0.000157 V

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Rutgers, The State University of New Jersey

Numerade Educator

University of Washington

University of Winnipeg

So we're asked to find the magnitude of the induced M F in the square conducting loop surrounding the center here of the soul annoyed. Okay, so the induced Ian meth, of course, is expressed as or it epsilon is equal to the changing magnetic flux belt. If I divided by the change in time Delta T Okay. But FYI here is equal to the magnetic field times the area in which it's going through. Okay, The magnetic field is equal to mu, not which is a constant just the permitted ity electromagnetic permitted V of free space. You can look it up, but it's equal toe four pi four pi times 10 to the minus seven test Last times, meters squared per ampere was very common again. You can look that up if you want to know more about it multiplied by the number of turns per unit length multiplied by the current I Okay, so that's the magnetic field. And then the area here is pi r squared so that all that is multiplied by pi r squared. Okay, so, plugging these values in for the induced e m f. We find that Absalon is equal to well these air Constance, you not as a constant so we can pull that out. The number of turns per unit length there's a constant pie is a constant R squared is a constant. So really, the only thing that is changing here is the current dealt I with respect to time Delta T, which we're told is 28.5 amperes per second. And we know everything else in this expression. So plugging those values and we find that this induced IMF is 1.58 times 10 to the minus four volts, we can go ahead and box set in is their solution to our question.