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#ire side - OU cm placed uniform magnetic Iield magnitudt directed Into (hc paqe square turns &no Iusetance 0.780 If the coil rotated throuat Anale about the ho...

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#ire side - OU cm placed uniform magnetic Iield magnitudt directed Into (hc paqe square turns &no Iusetance 0.780 If the coil rotated throuat Anale about the horizontal axi5 ahownthe figurc stowm belor- The coll nat 0.335 Find the followlngKulatona(0) the maonitudcuverudt &m nduccdthc coil during thls rotution(0)lne everaoe cutrent Induced tne coil durina tharetalion

#ire side - OU cm placed uniform magnetic Iield magnitudt directed Into (hc paqe square turns &no Iusetance 0.780 If the coil rotated throuat Anale about the horizontal axi5 ahown the figurc stowm belor- The coll nat 0.335 Find the followlng Kulatona (0) the maonitudc uverudt &m nduccd thc coil during thls rotution (0)lne everaoe cutrent Induced tne coil durina tharetalion



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ssm A circular coil $(950 \text { turns, radius }=0.060 \mathrm{m})$ is rotating in a uniform magnetic field. At $t=0$ s, the normal to the coil is perpendicular to the magnetic field. At $t=0.010$ s, the normal makes an angle of $\phi=45^{\circ}$ with the field because the coil has made one-eighth of a revolution.
An average emf of magnitude 0.065 $\mathrm{V}$ is induced in the coil. Find the magnitude of the magnetic field at the location of the coil.

Hi and given problem number of terms in the closed oil are given us and is equal to five country area of cross section of this coil is a is equal to four centimeter square or we can say this is for into and it's one minus four metarie square resistance. Effective resistance of the coil is 50 oh and a magnetic field in which this coil is rotating is given as 0.2. Their birth parameter is quite. It is given that initially the plane of oil was perpendicular to the magnetic field means you can say area after was parallel to the mat. Beautiful. Better hands angle between them or zero degree. And then this coil is rotated through 1 80 degrees. So the final angle between them will become 180 degree. So as for Faraday's law of electromagnetic induction, MF indios in this coil will be given by absolutely is equal to minus and dimes the time rate of change of magnetic flux link through each turn. Or it can also begin as minus and times of by two minus 51 Whitey. Or using the expression for the flux it becomes as the fluxus be dot or be a cost center. So this is be a cost. He Tartu minus B. A. Cost Tavern final flogs minus initial flux divided by time at this time is given here. Our time has not been given to us. No taking this B. And also as a common out we get this expression for the EMF induced minus N. B. A. Into cost theater to minus course peter one divided by time. So now current induced in this coil will be given as using arms law, I is equal to EMF induced divided by resistance means this is I is equal to minus N. B. A. Into cost. He Tartu minus cost. He taught one divided by he and into our for the resistance. Now using the basic definition of current, it will be given as the time rate of law of judge through that conductor miscue by T. Which finally cancels this time here. So finally an expression for the charge will be given by minus N B. A. Into cause it are too minus scores one and divided by our finally plugging in all the known values here for a number of times this is 500 magnetic for 0.2 Tesla area 4 to 10 to the par minus four m square because one a Hillary 42 or two minus course zero degree 40 to 1 divided by resistance which is if the own. So finally here it will be minus eight into 10 regional part minus four bracket minus one minus one Poland. Or we can say this charge is 1.6 into 10 days, par minus three column, or 101,000 and 600 taking three more decimal places towards right, it becomes standish for minus six Fulham or finally, this is 1600 micro column. The charge passed through this coil when it is rotated from zero degree to 1 80 degrees. Thank you.

High. In the given problem there are two identical circular toys which are having the same area of protection and same number of terms in them carrying the same magnitude of electric current. Mhm. So these are the coils, the circular boys called A. And coil B. Mhm. This is called A. This is called B. Both are having their damages along X. X. Is and why taxes this first coiled coil A. Is carrying the current in clockwise direction and Colby is carrying the same current. But in counter clockwise direction area of each chord is given to be a. A number of terms. Yeah, in the in each one of them is equal to both of these goi coils can be rotated about X. Axis. No. In the first part of the problem we have to find the directions of magnetic moments associated with these girls and we know magnetic moments. The directions of magnetic moments are always true. South ball. Mhm. Do North Pole. No. Yeah. Upper face of quality. Mhm. Mhm behaves like Mhm. South pole as the direction of current in it is clockwise, so it will behave like South pole. So the lower face which is not visible to us, will be behaving like a north pole. Hence the direction of magnetic field magnetic moment. So the magnetic moment. Oh this coil will be from south to north means will be in Judah plane of paper. Mhm. And for called a sorry for Colby. Mhm. As the upper face is getting the current n counterclockwise direction. So it's a perfect place. Mhm will behave like Yeah, not all. And as the direction of pancreatic movement is from south to north, so it will be coming up. So magnetic moment of course I'll be okay, will be coming out perpendicular to the plane of paper. This is the answer for the first part of the problem. Now in the second part of the problem, we have to show that these two coils are in rotational equivalent for which we will find the drug experienced by these two coils so taught experienced by calling a premium even by in vector form. This has given us the cross product of magnetic moment with the magnetic field as the direction of magnetic free. For both of these calls is coming out for particularly to the plane of paper. As it is given that the magnetic release along positive said access means for both dark oils the magnetic release coming out. So for going a as the magnetic woman is involved into the plane of paper and magnetically is outward out of the plane of paper. So if I use the rule for the cross product, consult to be new in to be in due Scientific data. And that data will be 180°.. Will consult with the new into be into sign 1°.. So the talk experienced by the school will be zero note protecting on it. So the oil is in rotational equilibrium. Now for coil P the torque experienced by coil B will be P is equal to again using the same expression New cross B. As for what will be, the magnetic moment is outward and magnetic field is also outward. So the angle between them is zero degree. Hence we can say this to be Which is given by new into be into sign 0°.. So it will come out to be zero. So the idea is also in a rotational equilibrium. In 3rd part of the problem, we had to find the expressions For the magnetic energy store in these coils. 3rd part of the problem, the potential energy is given by U. Is equal to minus new dot be so for the first white you A. Is equal to minus mill be into cause angle between them which is monetarily. So here it comes out to be you A. Is equal to minus New into be into minus mint. For cosmo 90 degrees. Would consult to be you a sensible to new into the Similarly on the 2nd coil you'll be having the same expression minus new dog. Be as the magnetic moment is in the same direction as that of the magnetic. So this is new in to be into cause zero degree. So this is you be a secret minus new times the magnetic grid. Answer for the third part of the problem. Now in the fourth part of the problem, we have to find which of the coil is in stable equilibrium and which one is in unstable equilibrium. So as the angle between the magnetic moment and the magnetic field is wanted to read for A. So we can say oil A. Is in on a stable equilibrium. Mhm mm. Probably be is in stable equilibrium. So these are the answers for the given problem. Thank you.

Okay discussion is from the helm holds coil. So there are there is a pair of two identical flat circular coils like this. Okay. And these are the points Okay and these how the radius are? Okay and the distance between these two are also are Okay so there is a midpoint in between these two coils. Okay. And what are what is given? Okay. Each the circular coil of wire. Each 500 tons, so and is given 100 okay. And the radius of 0.5 m. So our is given 0.5. Okay. And the coil are arranged as the set of Helmand's coil. Okay, parallel and with the separation of 0.5 m so they are is again the separation is 0.5 m if each coil carries a current of 10 mps so I is given 10 m pierre so determine the magnitude of the magnetic field at the point on the common axis of the coil and halfway between them. So at this point. Okay, So we can say X will be our by two hair, understand so no problem. We know that the magnitude of the magnetic field can be given by. Okay. Further there is um you note I Squire divided by two X. Square plus R squared. Okay. But there are two players. So it will be multiplied by two and it is only for one turn. But there are uh there are 100 tons. So we will multiply it by and understand. So this will be the formula for hell holes pair. Okay you can also learn this formula. So now we will uh put the values here to first of all to will be cut and because two new not I ari Squire and divided by axes are by two. So it will be oh sorry it's raised to the party but it was also there. Okay. So it will be are required by four plus. Are required. So it will be five. Are inspired by four holders to the power three by to understand. So when we saw it will be new and I ari Squire divided by ari Squire raised to the power three by two. It will be our cube. Okay. And five by four raised to the power three by two. It will be 1.40 understand. So here numerator are square denominator, argue so it will only one are in denominators. Some you note and I divided by 1.40. R will be the magnitude of magnetic field. Okay, so we will be now we will put all values here. First of all. New, not that is four pi multiplied by 10 raised to the power negative seven. It will be Tesla meter par mps. Okay. And any number of times that are 100 multiplied by that is current. That is given 10 ampere divided by 1.40 r. That is radius, it is given. Okay, zero point five me to understand. So when we solve it will be well saul using calculator, it will be 1.80 multiplied by 10 raised to the power negative three Tesla. And this will be the final answer of this question. Thank you.

This is Chapter 27. Problem number 44. We have two coils. One is carrying for walkways. Parent. Um, we call this coil a when we haven't looked Room that has current along the opposite direction for B Um, the magnetic field is out of the page, so the green is the magnetic field B and in part A, we are actually asked to determine the direction of the magnetic dipole moment sector. It's going to be equal to end by times A is, you know, So from right hand rule, bye aligning your fingers along the direction of the current your thumb is going to show the direction of the magnetic moment factor. So for a than near is pain to the page where B is going to be the direction of the magnetic tackle moment is going to be out of the picture, get from the right hand roll he could be. We are asked to calculate the torque network on each coil. So again, the magnitude of the torque in terms of the magnetic moment and the magnetic field is the vector product cost product of new and be vectors. If you're going to write the magnitude of the Torp. Then it's new, be signed data. Then we're gonna have to determine the angle between you and be for each case. So for a for example, we said that direction of Mu is into the page. But we know that the direction of be sorry not to make this, uh, Green this is the direction of the no matter what, so you can see clearly from here that for a the angle between the two is one a day sign 1 80 year zero. Therefore, the network is zero for B. It's a similar outcome because the angle between the two, the parallel with respect to each other, the angle between two is going to be zero sign here is going to give us zero. Therefore, the torque network home, the coil me is gonna be cool to zero in part C, Whereas to calculate the potential energy for each coil new dot Be right using this formula. So again you be callsign data. Now we know the angle between you and be right there here. So, for hey, uh, oil A again, data is 1 84 sign 1 80 is negative one. So you is gonna be negative. B times negative one positive U B for oil A then for a crowd of people home science. Since the angle between the zero, Los Angeles is going to give us positive one. You is going to be equal to negative as we can, positive one itself. So we have, um, positive potential energy for coil A and negative potential energy for coil B. No. In party, we have this discussion about stable or unstable equilibrium. Um, just let me remind you what a stable equilibrium is. We say that the system is unstable equilibrium when the system is displaced from equilibrium. If it experiences a force or torque in a direction that is opposite to the direction of displacement, then we say that the system is in stable equilibrium. So for our case, the coil that is in a stable kilogram, yeah, is the one that has the negative potential energy, which is the coil see and unstable equilibrium because he picked up on it happens off the exact opposite way. Um, when we have an unstable equilibrium. So when coil be sorry, coil A is displaced from equilibrium, it's actually not going to go back to its original um, rotation. On the contrary, it's going to be the it's going to be along the opposite direction, so and that corresponds to the higher potential energy.


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