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Magnetic field, is perpendicular the page, shorm B is in tesla Ayhen is in meters. & is a positive constant: metal rod slides the right along the conductive rai...

Question

Magnetic field, is perpendicular the page, shorm B is in tesla Ayhen is in meters. & is a positive constant: metal rod slides the right along the conductive rails, with canstant speed At t = serands it is passing #-Ja Find the EMF induced the loop at t = (b) Clearly indicate the direction the current in the loop? Your answver should be in terms of and our usuae constants

magnetic field, is perpendicular the page, shorm B is in tesla Ayhen is in meters. & is a positive constant: metal rod slides the right along the conductive rails, with canstant speed At t = serands it is passing #-Ja Find the EMF induced the loop at t = (b) Clearly indicate the direction the current in the loop? Your answver should be in terms of and our usuae constants



Answers

A square wire loop with $2.00 \mathrm{~m}$ sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field as shown in Fig. $30-43 .$ The loop contains an ideal battery with emf $\mathscr{E}=20.0 \mathrm{~V}$. If the magnitude of the field varies with time according to $B=0.0420-0.870 t,$ with $B$ in teslas and $t$ in seconds, what are (a) the net emf in the circuit and (b) the direction of the (net) current around the loop?

Okay, So for this one, we have a loop. The battery that's partially submerged in a magnetic field. That's all to know that the magnetic field would be Ah, blue sari. Um, very synesthesia ish. And B is luckily blew. Some magnetic fields are always blue for me. Okay, so the magnetic field is out of the page, and we're told that this loop has sides of two point. How many zeros is that? Let's see. Let's see, Ooo meters. And we're told that B is equal to 0.0, for two zero minus 00.870 T. The field is decreasing. And then this the IMF is of the battery in the loop is 20.0, goals. And I think that's all we need. Okay, great. And so the questions asks, What is the IMF induced, um, are extremely ask first. What is a natty EMF in the circuit? Okay, so there's already an EMF from the battery, um, and then something called u M f bap. And then there's an additional AM F because we're changing the flux. And so, uh, bye. Faraday's law. We're gonna have a change in. All right, we're gonna have a induced enough so can use our familiar formula hopefully induced a few times your, um, at this problem. And so that's gonna be the time derivative of the magnetic flux, which is be a way. Is the area intercepted? Um, by the flux by the by the field. And so that area is constant, and it's just gonna be l squared over two weeks, only half of the squares in the magnetic field. And then we're left to just evaluate the derivative of be with respect to time. And, uh and so, yes. So now we can say that D b e t t ISS minus point a 70 there, that eight backwards. Okay, so Ah, negative, constant. And so therefore, this is, uh yeah, So we would plug this in here and then plug in Ellis two meters into here. When I did this, I obtained that, um, the M f was 1.74 worlds. And so on a comment on the signs. Um, so we got a positive number, and that does actually indicate the direction, but the current flows, but I think that the easiest way is to know, like, learn the formalism of what what the meaning of a negative and positive number is. Although, if that appeals to you, of course you can read about it. I'm gonna do it from the approach that I would use Thio t think about this because I agree. You know, we have a c in math in. Is this e m f gonna go opposed the battery Or is it going to add to the battery? And you want to do this through a kind of I I consider it a more narrative page based approach. And so, basically, let's look at the let's look at the physical situations we have this Byfield The Byfield is decreasing in magnitude. And so the loop wants to induce a current to keep it the same. It's always a sort of like restorative force. And so the bso, the bees going down. So we need We need this Luc to try to make it be that goes up. And so, um uh, are out of the page. Excuse me. And to do that, we would drive a current that's counterclockwise. And for a current to go counterclockwise Ah, that corresponds to an e m f. That's along the same directions a battery? Because the battery also would drive a counterclockwise current. So you can say I am asked. Net is 21.74. One quick thing. Um, okay. And yeah. And so it's gonna add to the current to the to the image of the battery and therefore cause a counterclockwise current. So maybe I'll kind of box thes so that they're totally clear, so counterclockwise. And then I get that for the net enough because I added the battery to the to the imam induced double chuck bees out of the page and then be is decreasing, okay?

Hi the given problem there is square shaped loop. The loop made up of a conducting wire. This loop is square shaped loop is arranged such that it's sides are lying along X and Y. Exit. This is X axis and here this is by access length of the square loop. That is given as L. is equal to 2.0 Centimetre. Or we can say this is 0.02 meter. There is a magnetic field in this region which is varying along the X axis, the direction of this magnetic really is out of the plane of paper. So it is coming out of this loop. Also, if magnitude is varying along the why it says the magnitude is going on increasing if we look carefully and this magnitude is changing with the passage of time as well. So there is a 2-fold change in the magnetic field which is linked through this flu expression. For that magnetic field has given us 4.0 be square. Why now we have to find the EMF induced in the slope at a time. E. Is equal to 2.5 seconds. First of all, we consider a small angular strip within this loop having are ripped IVE I. And at a distance of Why from the X axis small great having in finite is really small to be considered as a script. It didn't. The loop having a deferentially small with dy and limb. Many of course it's length will be equal to the side length of the square and length L. And it is that understands Wife on the X axis. So differentially small area of this strip. Actually, we are considering this square to be made up of infinite numbers of such streets and out of those a large number of strips we are choosing a single strip actually stands Why from excesses. So it's a differential E small area will be given as be A equals to land. It is L. In two words it is divided so deferentially small magnetic flux linked through this small strip will be given by defies equal to magnetic field. The product of magnetic field with the area. Or we can say this is the dot product is scalar product of magnetic vector the area better. And here it will be B. D. A. Cause zero degree because magnetic Elise perpendicular to the area element The angle between magnetic director and area were probably become zero And the score zero is one only. That's what this is b. d. a. Or we can say this will be poor piece where Y. And the white. So total floods on an average which is linked through this is where you will be given by integration. Integration of four. These were Y. L. D. Y. And the limits of wife from zero means when the street is at X axis two L penned, the script is farthest from. It's sexist. Taking the constants out which includes four piece square into L. We get it with the integration of why with respect to divide. So now when we apply the rules of integration We will get four E square into L. Integration of why will be by square by to enter the limits of Y from zero. To help. Well finally using these limits, we get an expression for this flux magnetic flux linked with the coil to be equal to E square into. Thank you hands. Finally using paradise laws of electromagnetic induction. The magnitude of EMF induced in this loop, square ship loop will be given by differentiation of magnetic flux with respect to time and this differentiation will be they are L cube being a constant, will be taken out, then we will differentiate and the school also will come out. So this will be the differentiation of the square. This differentiation will become, this is to L. Q. And the differentiation of peace. Where is too he? No An expression for um if induces four L. U. P. So finally plugging in all known values here, this is 0.02 m, you or the side land. And for time that was given a school .5 seconds. Finally MF induced through the slope At a time, 2.5 seconds come south to be 8.0 Into a 10 for -5 goals. Which is the answer for this. Even problem here. Thank you.

In this problem, on the topic of induction, we are shown to straight conducting rails that form a right angle A conducting bar in contact with the rails, starts at T. Is equal to zero at the vertex and moors with a constant velocity of 5.2 m per second along them. We have a magnetic field of magnitude 0.35 Tesla is that is directed out of the page, and we want to find the flux to the triangle formed by the rails and bar at a time of three seconds. The MF around the triangle at the time. And then we are told that if the E. M. F. Is a. T. To the power N A N N. A. Constance, you want to find the value of N. Now the height of the triangular area enclosed by the rails and the bar is the same as the distance traveled in time T. Which is D. Is equal to V. T. Where V is 5.2 m/s. We also know that the base of the triangle is to D. And so the area of the triangle A. Is equal to a half base times height, which is a half times two VT times V. T. Which is v squared T squid. Now, since the field is uniform, 0.35 Kessler's, then the magnitude of the flux five B is equal to the field strength B times the area A. And this is zero 35 Tesla's Times the area which is v squared, 5.2 meters per second squared times the time T squared, which is 9.46 T squid. So if we evaluate the flux at a time of three seconds, we get this to be 85 0.2 weapons. Yeah. Yeah, mm. The magnitude of the E m f is epsilon by Faraday's law is equal to the rate of change of flux. Defib D t is equal to nine point 46 D by d t of t squared. And so the i m f ε is equal to 18.9 t. And so if we evaluate this e m f at a time of three seconds, we get this to be 56 0.8 volts. Yeah. Now from part C, we can see that the value of N is one. Yeah.

Hi there is a square loop. Given problem is arranged in our uniform magnetic field has shown here in that give anything is having a cell also and we mm the uniform magnetic field is not linked and entirely through this is fresh able to what it is linked only through upper huh of this is square blue side off the square loop is even as and that is the L That is equal to 100 meter No area of the loop aid. That will be given as square off site and magnetic field which is varying as a function of time is given as And that is coming out of the plane of paper. This magnetic field and it is very with respect to time as 0.040 Tesla find us 0.870 Tesla for second In two T 34 times. So the magnetic flux and this we are doing for the first part of the problem a magnet blocks link to be blue will be given ass area of the lube which will be half of the area of the completed square effective area of the law into stagnated. E. Cool, we may have this as Y is equal to elsewhere and for Elvis's opens kilometer The Squire divided by two. And for magnetic field this is 0.0 Or those zero Islam 0.870. Tesla was taken into t know where it will remain as only then funding the spread it We care 0.08 or zero. Tesla minus 1.74 and it will not be as la. Now this is their birth. A unit of magnetic 0.08 for weber minus one point 74 Netbook 1st, 2nd in two D. Hence using Faraday's laws of electromagnetic production. EMF induced in this law will be given by -15. I did. Time derivative of the function of the magnetic flux. So if they differentiated here, The differentiation of first time will come out to the zero as it is a constant. Then differentiation of second term, it will be -1.74 into one only for the differentiation of tea with respect to time one only. So finally this Yemen indios in the coil comes out to be 1.74. Or and this EMF induced in the coil find its direction as the reason behind its induction is outward magnetic flux outward magnetic. No, that is decreasing the time. So as per lenses law, the Hindus magnetic field will also be outward but increasing so to have outward magnetic field is facing a purpose of the coil to start behaving life north pole as you know, Mcgrady field comes out of the north pole, the direction of current in it To be counter clock five as the direction of karate is counterclockwise means it is like this and means the E. M. F induced will be sending its current in the counterclockwise direction. And this applied. E M F is also sending the currently in counterclockwise direction means both the E. M. S are in the same direction. Oh Hindus NF and applied mm old. Are the scene Found 3rd Clockwise Direction. To get the IMF in this loop, both of them will be ready. No, well we can buy E. Is equal to 20.0 gold which was applied Plus 1.74 which was induced. The answer for the first part of this given problem is 21 .74 Pole. No, the second part of the problem, we have to find the direction of quarantined used in the loop and we have already seen it direction of or quarantined use in the loop. That is counter clock. Why? Thank you


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