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Oarallectors carry equa currents3.20The figure belowthe conductorscurrent directionthe page pointsand outpage atCalculate the magnitude the magnetic field point loc...

Question

Oarallectors carry equa currents3.20The figure belowthe conductorscurrent directionthe page pointsand outpage atCalculate the magnitude the magnetic field point located the center the square edge length200 M;Determine the direction the magnetic ficld point the leftlocated the centerthe squarecdge length0.200the rightuowarddounwardinto the page the page

oaralle ctors carry equa currents 3.20 The figure below the conductors current direction the page points and out page at Calculate the magnitude the magnetic field point located the center the square edge length 200 M; Determine the direction the magnetic ficld point the left located the center the square cdge length 0.200 the right uoward dounward into the page the page



Answers

Four long, parallel conductors carry equal currents of $I=5.00$ A. Figure $\mathrm{P} 30.32$ is an end view of the conductors. The current direction is into the page at points $A$ and $B$ and out of the page at points $C$ and $D .$ Calculate (a) the magnitude and $(\mathrm{b})$ the direction of the magnetic field at point $P,$ located at the center of the square of edge length $\ell=0.200 \mathrm{m} .$

Hi. In the given problem before long current carrying conductors are put at the ages Saw at the corners off are square Yeah, like this The square is named as a be see and d Then the cross sections off. These four conductors are shown as here This is the conductor put at a which is carrying the current in a direction perpendicular to the plane of paper directed into it. Then the conductor at sea is carrying a current coming out off it. Then the conductor at B is carrying a current getting again into it. And the conductor at D is getting a current again coming out of the plane off paper or particularly, the side length of this square is 0.200 m. So we have to find the net magnetic field at the center. Off this square, we have to find the magnitude and direction off the net magnetic field. At this point B the magnitude off current in all these four conductors, This same which has given us 5.0 and peer and the distance off this observation point B is also same from all these current carrying conductors which is given ass the half off the diagonal lint. This is the half of diagonal length, and we know the diagonal length has given us side multiplied by square root society to it is given as then by two. So the diagonal land will come out Toby 0.200 into route to and then it's half will be by to. So finally, this distance off observation point from all four current carrying conductors is given a 0.14 14 meter and as the current is same and the distances same so we can see the magnetic field Do do all these four current carrying conductors at the center will be having the same magnitude. So you can say be a is equal Toby, be physical. Toby C is goingto be D, which has given us new not by four pi into two. I buy art or we can say this is Standish Par minus seven into two into five m p. R. Divided by R, which is 0.1414 m. So finally the magnitude of this magnetic field comes out. Toby, seven point 07 in tow, 10 dish par minus six Tesler. Now, now we will look for their directions off all these magnetic fields. So first of all, looking at a and using right hand come ruled the direction off magnetic field due to this current in conductor put at a will be towards the point to be Yeah, so this is be e. And if we look for the magnetic field due to that current carrying conductor put at B, this will be the words Be so here. This is B because off B, then if you look for B here, a magnetic field at point feed uto current cannon conductor passing through the will be also towards B So this is the D. And finally, if you look for the direction off magnetic field you do while passing through C, that will be the works D. So this is B. C. So impair the two magnetic fields will be joined. So finally we can say the net magnetic field due to A and D will be equal to the net. Magnetic will do to be and C as thes two are in the same direction. Hence we can see it. It will be two times off 7.7 into 10. Dish par minus six. Tesla or it becomes 14.14 into 10 days. Par minus six Tesla. So it can be represented like this. So these are the two magnetic fields here. We can see each off the spare Toby B dash. So this is B Dash. This is also be dash and the angle between the diagonals off a square we know is given as 90 degree. So finally, the net magnetic field will be given by the vector. Sum off these to be dash and the direction off. This will be like this in the plane of paper towards the bottom off the paper. This will be the net magnetic field. So expression off this net magnetic field will be squared off. B dash, Let's to square off. Barash having a square root so we can see this is two times off square off the dash. Or finally we can say this is V dash route to So this is 14.14 into 10. Dish par minus six Bruto Esler. So finally, the magnetic field at the center of the square comes out Toby 20 into 10 dish par minus six. Tesla's or we can say this is B is equal to 20 my Croat Isla in a direction towards the bottom, off the page and in the plane off page. Thank you.

For this problem on the topic of magnetic field, we are shown for parallel conductors which carry equal currents of five mps and we can see an end view of the conductors. The direction of the current is into the page at points A and B. And then out of the page at C and D. We want to find the magnitude and direction of the magnetic field at Point B, which is at the center of the square with edge length 0.2 m. Now, each wire is distant from P by a distance of zero point two m times the co sign of 45°.. And this is equal to the distance from the center of one .141 meters. And each wire produces a field at P. Of equal magnitude. In this field, B. A. Is equal to you know what I over two pi A. And this is equal to two Times 10 to the -7 Tesla meters per ampere. I'm the current of five mps divided by zero point 14 one meters. And so this gives us the field strength produced by each current To be 7.07 micro Tesla, now carrying currents into the page A produces a field of 7.7 micro. Tesla is to the left and down at an angle of minus 135 degrees. B. Creates a field to the right and down at minus 45 degrees, Carrying a current towards us. See producers, they feel downward into the right of -45° and these contributions downward into the left. and so therefore the total contribution is four into seven point zero seven Micro Tesla's times the sign of 45°, which gives us the total contribution at point p From all of the currents to be 20 micro Tesla toward the bottom of the page.

For this question. We're considering four long parallel conductors, each with the current I of five amperes. You can reference figure p 19.49 to get a look at this. Um, the direction of the current is into the page. Appoint a M B and out of the privilege of point, C and D, and it's asking us to calculate the magnetic field in direction of magnetic field a point p located at the center of the square with an edge of 0.2 meters. Okay, well, in general, the magnitude of the magnetic field be by a long straight wire could be calculated as such, B is equal to community times. I divided by two times pi times the distance for calculating the magnetic field away from the wire. I deep Okay, So in our situation to calculate the man into indirection magnetic field a point p, we're gonna consider that the distance of the point p from each wire D is equal to using the dagger, and zero D here is equal to the square root of well over two squared plus l over too. I swear. This is because if you look at a square here. I'll just do a little rough sketch here. If you look in a square and want to consider Pythagorean theorem were at some point in the middle p we can break it up like this, and this gives you a right triangle. So this distance here would be l over too. This distance here would be l over too. And what we're really trying to find is this distance here D At this rate angle, the reason those two are l over to is because the total length of the Sinus l when we just cut the length of the sides and half. So that's where that came from. Um, so we can plug that into our value for deep when we find that be here is equal to 7.9 times 10 to the minus six. Tessa. Okay, but that's just for 1.3 identical current is passing through all the wires, though all four wires. Therefore, the magnitude of the magnetic field at point P is the same due to all four wires, that is B. A magnetic field from wire A is equal to the magnetic field from wire B B B is equal to the magnetic field. From wire. C BC is equal to the magnetic field from Weir D B D is equal to magnetic field. Just calculated beat. Okay, so the sum of the magnetic field from B A and B D cause we need to remember here that what we're told in the beginning is that A and B are in the same direction and CND are in the same direction. So let's consider the magnetic field from from a nd. So it's given your page going here, we'll call this magnetic field be 80 and it's just simply equal to magnetic field for May plus the Magnetics That right, that literally plus the magnetic field from me. But we're told that both of those were just equal to the magnetic field. Be they'll be calculated in the beginning, so this is just equal to to be. And then now the magnetic field for BC again, we're told that these are both going the same direction, so we have B B plus B C. When this is also equal to to be okay. So now to get the net magnetic field, since they're flowing in opposite directions, we can once again use a degree in Europe. So we have the square root of B A D Square plus be BC square So, what we find here again B A, d and BBC, or each equal to to be and be here, is equal to 7.9 times 10 to the minus six Tesla. So you plug those values in and you find that this is equal to 20 times 10 to the minus six Tesla or 20 micro Tesla. You can write it either way, but we're also asked to find the direction well, according to the right hand rule from each of these wires, the finger or the thumb from the right hand point in the direction of the current in the wire, the fingers point in the direction towards the point we're wanting to calculate when you curl your fingers. That's the direction of the magnetic field. When you do that in this situation, you find the magnetic field here is in the downward direction so we can say downwards. Let's go ahead and boxes in as our solution to the question

This problem. Cause the concept of the magnetic field produced by your current carrying wire. And to solve this problem 1st, the need to define our coordinates access along the right direction. We consider watch two X. And along the top of the page. We consider or still by direction. Since the point is in the center of the square the distance of the point P from each. What is this will be seen. And let's say the distances are that that will be cuba into the side length of the Squire. One route. Okay. And the magnetic field produced by the each wire on the vortices cutting equal current. We can write the magnetic field placed by the each bias may not into I upon to buy into art that is airborne row two or we can practice us may not i upon uh Route two times by a. That's it is such a question. Now if we analyze the direction of the magnetic field produced at point P. So due to the point E the direction of the magnetic field produced is along the direction along B. It is that this is due to the via a. And on point period to the vibe. The magnetic field direction is towards the similarly go to see the direction of the magnetic field on point B is towards deep and due to the wide the direction is to R B. Okay, this angle Will they? 45°. Okay. So by cemetery we can see the net magnetic field along X direction will be zero. So by symmetry. Mhm. The net magnetic field along X will be zero. And the magnetic field along y equals- of four times B uh Costs 45°. And B. Is the magnetically produced by a single wire. Or the magnetic field along the Y. Direction equals minus or four into may not I upon route to buy a It took us 45 which is the equivalent of one upon. Or the magnetic field along the Y direction is- of two. May not I am born by E now substitute the value and find them ah magnitude of the net magnetic field. So B equals Uh two into 4 piles in to tenders minus seven Tesla meters for MPO And the current in the virus five mps upon by and The side length is 0.2 m are the magnetic field produced. The magnitude is um two In to tenders -5 S. La. Or we can say the magnetic field is 20 micro Tesla along negative wife access. In other words, you can see the magnetic field is 20 Micro Tesla along the bottom of the feet


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