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D) 23AC 27AC0S (LT* 8 =| 44(6 C= Iak Toq QvBs n6 Use the following answer questions 16-17: lonk straight wire is camying cumut of5.0 Ain the direction shown in the ...

Question

D) 23AC 27AC0S (LT* 8 =| 44(6 C= Iak Toq QvBs n6 Use the following answer questions 16-17: lonk straight wire is camying cumut of5.0 Ain the direction shown in the figure. Thc point Pis 0.040 m from the wire0.04What is thc dircction of the magnctic ficld at point P due to the current in the wire? t0 tbe right of page tbe lelt of the page toward the bottom of the page into the plane of the pige E) out of the plane of the pagePage

D) 23AC 27AC 0S (LT* 8 =| 44(6 C= Iak Toq QvBs n6 Use the following answer questions 16-17: lonk straight wire is camying cumut of5.0 Ain the direction shown in the figure. Thc point Pis 0.040 m from the wire 0.04 What is thc dircction of the magnctic ficld at point P due to the current in the wire? t0 tbe right of page tbe lelt of the page toward the bottom of the page into the plane of the pige E) out of the plane of the page Page



Answers

Eight wires cut the page perpendicularly at the points shown in Fig. $29-70 .$ A wire labeled with the integer $k(k=1,2, \ldots, 8)$ carries the current $k i$, where $i=4.50 \mathrm{~mA}$. For those wires with odd $k$, the cur- rent is out of the page; for those with even $k$, it is into the page. Evaluate $\oint \vec{B} \cdot d \vec{s}$ along the closed path indicated and in the direction shown.

Hi in the given problem, the two straight parallel current carrying conductors are yet such that they are perpendicular. The plane of paper in the wire, one the first conductor. The current is coming out of the Pelino paper and the direction of current in the conductor too. That is not given in the beginning gap between them. He's given us and centimetre. Then an observation point B is at a perpendicular by sector of this line joining their book conductors, such that if we join across sections of these two conductors with this observation point angle between these two lines is given as 90 degree. So here this is 90 degree. This is perpendicular perpendicular by sectors. So each of these two angles will be 45 degree each. This is 45 this is nineties. So clearly this angle here will also be 45 degrees. This distance will be half of 10, means five centimeter. You know, this strangle will also be and I Socialist right angle triangle. And see if this is why this distance will also be filed. So finally we can see if you consider this wire to be situated at point you this wire to be situated at point R. Then PQ is equal to P. R. And that is equal to square root of 50 centimetre. This is five, this is five. Then using pythagoras. Tehran square root of every centimeter will be this hyper tennis. No, in the first part of the problem if good on in via to is outward out of the plane of paper then using right and come rule the directions of magnetic feels the one magnetic field due to the current environment and B two magnetic field you to quarantine wire to at point B will be as shown in the figure. So using their right and thumb rule considering the current environment which is coming out of a plane of paper the direction of this magnetic field that point he will be like this. This is the one and you too the current environment which is also coming out of the plane of paper. That will be yes this is B. Two. And using the symmetry of these angers angle between these two magnetic fields is also equal to 90 degrees. Now magnitudes of these two magnetic fields will be equal because the currents in both of the virus is same and understand speak U. Is equal to P. R. And that magnitude will will be given by mu note by four by into two. I buy. Oh were this distance square root of 50 centimeters is equal to our Now plugging in all known values here for Munich upon four by the standish par minus seven islam meter perimeter here multiplied by two times of current and current here It's given us 100 ampere in both of the wires and then the distance which is the square root of 50 centimeter or it's quite out of 15 to 10 days par minus two m. In Tesla disagree measure. So finally these two magnetic fears comes out to be four into 10 par minus four. Invited by rubio S la. So net magnetic field having angle 90 degree between them. If we use parallel ground law of tradition, this will be the net magnetic field a long negative by access. So again using pythagoras here. Um, this will be given there as a square root of even his car. Class B two square as both the magnetic fields are same. So we can say in place of B two, we can use Beaven square, it will be twice or even square having a square root. Or we can say this is be even in two. Finally, we can say this is foreign to 10 for minus four, divided by two, multiplied by two. Tesla. Or in vector form we can see this is as it is a long minus Y. X. And so sorry, minus X. X. And so we can write it like minus pour into a 10 for minus four. That's la Oh you get Which is the answer for the first part of this problem? No, in the second part of the problem, if we reverse the direction of current in wire to so if current in wire to yes in world into the plane of paper, then the direction of magnetic reed due to this current will be changed if you don't this diagram again here again, this is why one carrying current in outward direction. But this is why getting currently inward direction. It says perpendicular by sector again, this is the observation point at which now we have to find net magnetic field. So here the direction of magnetic will do to buy one. That will be same as we have done in the first part of the problem, going like this be one, but now the direction of the two that will be like this as the current and the distances are still the same. So magnitude of these two magnetic fields will be still. The scene means four into tended bar minus four. By route to Tesla. Again, the angle between them 90 degree. So if we apply parallelogram law of tradition, this time the net magnetic will it will be having same magnitude means physical too. The one in two square root of two Tesla for direction it is vertically up means along positive Y axis. So we can say this is yes, 4.0 into tended bar minus four. Yes La G. Yeah. Which is the answer for the second part of this problem. Thank you.

For the given problem. A close look at the path reveals that only one, 36 and seven currents are enclosed. Thus noting the different direction described in a problem we obtained integral. Awful be daughter D s is equal to mu nod mine seven I minus six I plus three I plus I. This will give us a five from you know, Lord, I then substituting a value off a current in Nord, we get integral off a B Dawg D s. Is it cool to 2.83 times 10 to the power minus eight Tesla meter.

For the given problem. We know that this is distance from the each wire to be is our physical to do. Divide by square root off to which is equal to zero point 071 meter in both parts. The current Isaac All Thio 100 Pierre for a party off. The problem with the current Spangler application off right and rule um, which means to deter mined each of their contribution to the field. A to point B reveals that the word it'll components cancel in the horizontal component aid yielding the results, which is to be Is it called two times off from you? Nor die? Divide by two pi R times, of course, off 45. This gives us 4.0 times gentle power minus for Tesla, and this is directed in the minus. XX is direction in the unit factors we can write. B is equal to minus for times gentle power minus for Tesla in I kept direction for about B off the problem. Now with the currents anti paler, application off right and rule shows that the horizontal component cancel in the work will complement head up so resentful o gentle cancel word deco head so B is equal to two times off mu non. I divided by two by our sign 45 degrees, which gives us four times 10 from power minus for Tesla. And this is directed in a post to y direction in ah factor notation we can write four times 10 to the power minus four Tesla in Jacob direction.

So see over here we have our clothes such as is right on like this and very and you know that kind of car batteries like very kindly like this one. So over here there is a current I one I two I three I four I thought till I o one i 2345 for Android. So we have given that Over the current king the current the current I equals K. Times of I. And it is nothing but this number, this number I wanted to say this is 1128. And what more information we have is that we have. Is that that what what what what more influence than we have that the key and those which are old K are out of the pledge and those even care into the page. So for all the kids that is out of the kids. Okay. And for even this is into the kid and into the plane and even into the peso. However, how can we do that? So we know that we need to find them. Um That means were ideas. So what ideas by the NPR slow? We don't know that Well yes. You know by the Mps law that I need into area, I need him, I need him to I knew it into total total total parameters very media than himself. So I need to do nothing. But if odd number will be if we are taking out and that means are inside the plane or outside the plane is a positive. That wins one I I blustery. I plus five. I Plus seven I and -2. I plus poor I Plus six. I plus eight. I. So what will be 74 and 59 and 9716. I -8. So 6612 since 12 or eight 20 I into total. And tell okay so this will become nothing but minus of uh four I. L. And elegant Roland. And this minus indicate that we have taken inside the planet, positive uh outside the planet the politics. So they should be inside the plane direction. Okay?


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