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C5uMlcnold coil with length Luier Ut elKichetpjnsuceMUL field u [2Find the...

Question

C5uMlcnold coil with length Luier Ut elKichetpjnsuceMUL field u [2Find the

C5u Mlcnold coil with length Luier Ut el Kichet pjnsuce MUL field u [2 Find the



Answers

A rectangular coil with resistance $R$ has $N$ turns, each of length $\ell$ and width $w$ as shown in Figure P31.27. The coil moves into a uniform magnetic field $\mathbf{B}$ with a velocity $\mathbf{v}$. What are the magnitude and direction of the resultant force on the coil (a) as it enters the magnetic field, (b) as it moves within the field, and (c) as it leaves the field?

So according to Friday's Ella off electromagnetic induction, we can write and USDA MF as negative Read up change off flex And according to the definition off flags we have flex equal toe dot product off beyond a That is equal toe be a because I know Kita s is the problem. We are given that plane of qualities perpendicular to the magnetic felines. So the bacteria area off pulling up oil will be parallel toe magnetic field. So here angle between area victor and bees. Zero degree. This gives us flags equal toe be times air because I know off zero degree on because I know zero is equal to one So we will get flags is equal to be okay Now we can write induce enough equal toe minus do you by DT many times. And here is the surface area off putting off oil which is Costin's so we can write induce him a physical toe minus and toe db upon duty. So this gives us induced a Memphis proportional toe. The negative rate of change off magnetic field are we can, right? This is in Memphis proportional do Then I get you slahv off the magnetic field. Now here. Graph is plotted between time and magnetic field from zero to Taiwan. Magnetic flux. Sorry. From zero to T one. Magnetic field increases here. Slope of magnetic field is positive. Now here we can write from Gino Toe Dear. Magnetic field increases. So here we have so love off the graph. Positive. But we have a Memphis. The negative of the Slav. So here Mm will be negative. And from the 31 slow off the grafitti Constant. So here we will get negative I am of so we will get Ah graph. Like this far a members is time now In the second case from he won 32 magnetic field is constant. So here's lobbies zero This gives us and you see um Africa all too zero So from t one to t two, we will have in Africa will toe zero No from Ditto to t three. Magnetic field decreases here again. Slope is constant and negative, so we will have induce him off. That will be positive

Hi. In the given problem, this ISS, the magnetic field uniformed magnetic creek, which is directed into the lane off paper. And there is a coil, a rectangular coil having large number off turns. That's sure. Yeah, the number off turns in the koi is en the total resistance off the while used to make this coil is our the magnetic feared inward. Action is be the land of the oil he's in, and it's whipped is W. It is being pushed into this magnetic field are pending, really with a velocity V. But so as the oil will be entering into the magnetic figure this week, it will be intercepting the magnetic field lines perpendicular Lee, not the men. So the IMF, emotionally NFL being used across the Richt holy as the koi, we'll be entering into the magnetic field. It's Mitt will be intercepting the magnetic field lines perpendicular early. So the Emma feel being used across it only and this motion early enough in news will be given by the expression be into V in tow l and for length. This is W and S. The number of currents in the oil is in. So overall it will be given us end times off B the W This is the Iemma induced across the end off this are no The current due to this image will be given by hi is equal to yeah divided by the resistance So the net current will b and B the w divided by the resistance the total resistance Finally, the force acting on the soil will be given by be a magnetic field I the courage and the length which is again w And as the number off parents is 10 So the total number off the vets will also the end So the total force will become an times off This hence, finally, when we put all these values will get b times off N b the w divided by ah into w times And finally it becomes end squared Be sweat be w squared, Divided by R So this is the neck force acting on the court and s the coil is moving towards right, so ask for lenses law. This force should be in a direction opposite with the motion off boy. So it should do you left and the oil is entering into the magnetic field no in party. The oil is moving the dinner magnetic. Really? So in that case, no change off flocks will be taking place. Flux going through the court will not change now. So pen, the coin is passing proof the feet no change or flux. Magnate clocks will be bliss. So no Yemen hands no current and no force will be acting on the coy in the third part of the problem. Now the soil is coming off now Our magnetic field on the opposite side for gained a flux will change so again and he ever feel being used again. Our current will being used So again our force will act on this coil and his force will be having the same value The same expression and square BCE where the w squared divided by r And still as the motion of the koi is towards right, So this force will still the acting Do you left? Thank you

Our question is a viral flint. Help is painted from a circular boil of some tones. A current I. Is then established in the court and it is placed in a uniform magnetic field. Maximum dog that X. On the qualities we have to calculate. So from the question here, N. Is the number of turns and R. Is the radius of the coil. So we can put. The formula is equals two number of turns into radios to fight are so from here R. Is equal to the radius will become All over and to five. This will become our equation. one genetic field formula is given us A. I. And from here he is equal to by our square. So put this value of art. This equation one for this value in this situation that is It's where over four pi squared and and square. So then we get is any is canceled. High is cancer with this fight. And we get a square I. five and 5 four. Where M. Is the magnetic moment of oil here. This Esther magnetic moment. Of course for an empathy. Weeks maximum M. Good. The maximum when Number of turns is equal to one. So for test we get L. Is elsewhere. I. 45 by four. So dark formula is excellent dog would be a maximum into be signed. My introduction really sign 90. So this would be I ask where in the 45 We will sign 19 is wrong answer caramel cookie and scarcity with your friends. So do you think that would arms. Thank you

All right. So, um, the first part asks for, um ah, uh, part eh? Wants to know once wants to know the IMF induced in the coral when it is all inside the field. And so ah, the e m f induced. And the coil is, um, my photos law, the rate of change of magnetic flux. Ah, and so magnetic flux, if you'll remember, is a member of turns and the coil, uh, times, magnetic field strength, times area, times Coast, I fi which, if I win this case zero. So this term is not zero um, an area there of the coil. And so, for part a and part see, you have the same answer, which is that the meth induced to zero. This is because by is not changing. That's because look at this. The number of turns of coil is not changing magnetic field strengths. Of course, not changing when you're all in or all out an area of the coil is not changing either. So nothing's changing, and five five's not changing. Our ago. A meth induced is there. Point B, However, when the coil ist partially inside the field partially outside, we're gonna hear we're gonna say that X is equal to the length of the coil. It's in the field. Ah, uh, and the height is point point four meters or 40 centimeters. Ah, sir. Area is 0.4 meters times x or 0.4 Ex meter squared. Uh, therefore, pmf induced is ah defy t. So this is, uh, number of chances. One. So it's a duty to times bleak times, eh? Uh and so moving on to the next page, so dd Ah. So you pull out the beauty and you have dd t three times a 0.4 times x monogamy. What about the units? Just yet in here. So point for is a constant that's pulled out here. Toothy of point for it's gonna read that. But meters times be, um, times duty too of x d X duty, if you'll remember from dramatic equations, is just v the velocity. So what we have here is point for meters times booty just been Tesla's and times V, which is ah, speed of the coil. And so this is 0.4 meters at times 1.25 Tesler times 0.2 meters per second. The two centimeters per second for the speed giving us 0.100 faults for the IMF induced


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