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Problem 54 Hard Difficulty

A circular loop of wire of resistance $R=0.500 \Omega$ and radius $r=8.00 \mathrm{cm}$ is in a uniform magnetic field directed out of the page as in Figure $\mathrm{P} 20.54 .$ If a clockwise current of $I=2.50$ mA is induced in the loop, (a) is the magnetic field increasing or decreasing in time? (b) Find the rate at which the field is changing with time.

Answer

a. \text { increasing }
b. 62.2 T / s

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Video Transcript

so party were asked to figure out if the magnetic field is increasing or if it's decreasing with time. Okay, well, to figure out what the magnetic field is increasing or decreasing, we're gonna use lenses loss. So according to let his law, if the flux is increasing in a particular direction, the induced current makes the magnetic field direction such that it decreases the flux. So similarly, if the flux is decreasing, the induced current produces magnetic flux in such a direction that it increases the flex. Since the current is in the clock whites direction and our problem, the induced magnetic field will increase towards the page, which tries to oppose the change in the flux. So the original field is directed outward and decreasing, and therefore the induced magnetic field will increase with time. So for part a no, we can say that the induced be field, which is magnetic field, will increase with time. And, uh, we used len slaw to do this. Look, I got a page in a box set in there, so shoot for party. All right. And lastly, Carby Part B says to find the rate at which the field is changing with time. Okay, So to find the rate at which the field is changing with time, we can use the induced E m f is equal to minus the magnetic flux. The change in flux divided by Delta T. Okay, well, this is minus the flux is the magnetic field climbs the area divided by Delta T. Okay, so the area is constant, so this is equal to minus area times D B over DT. Okay, so now we ran in a room on this page, so we'll go to the next page. The induced ium f from homes law is equal to the current times the resistance, and this again is equal to minus the area times the change in the magnetic field with respect to time d b d t Therefore d b d t is equal to Hi. The curry times the resistance divided by the area squared. Well, area here is pi r squared. So, playing those values into this expression, we find that this is 62.2 times 10 to the minus three tests. Look for second or 10 to the minus three is Milly. So this is Milly Tesla for a second weaken box end, and as her solution

University of Kansas
Top Physics 102 Electricity and Magnetism Educators
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Liev B.

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Hope College

Aspen F.

University of Sheffield

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McMaster University

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