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18. (25 points) long (practically infinite) wire carries cumenf of 1 vertically towards the top ofthe page: 2) (15 points) At 4 distance of I0 cm from the magnetic ...

Question

18. (25 points) long (practically infinite) wire carries cumenf of 1 vertically towards the top ofthe page: 2) (15 points) At 4 distance of I0 cm from the magnetic field wire, what causes? the magnitude A direction of theb) (10 points) Ifan clecuron ICIMC 1.6022-19 €) moves at [,OOO I $ purallel Ikx cunrent j I0 cm the wire , what ; LIc meMIULt and dineclion oftx mnu euclic Toneinec from 4ncmlultbc Kife "

18. (25 points) long (practically infinite) wire carries cumenf of 1 vertically towards the top ofthe page: 2) (15 points) At 4 distance of I0 cm from the magnetic field wire, what causes? the magnitude A direction of the b) (10 points) Ifan clecuron ICIMC 1.6022-19 €) moves at [,OOO I $ purallel Ikx cunrent j I0 cm the wire , what ; LIc meMIULt and dineclion oftx mnu euclic Toneinec from 4ncmlultbc Kife "



Answers

Two long, straight wires parallel to the $x$ axis are at $\mathrm{y}=\pm 2.5 \mathrm{~cm}$ $y=\pm 2.5 \mathrm{~cm}$ (Figure 19-44). Each wire carries a current of $16 \mathrm{~A}$ in the $+x$ direction. Calculate the magnetic field on the $y$ axis at (a) $\mathrm{y}=0, y=0$, (b) $\mathrm{y}=1.0 \mathrm{~cm}, y=1.0 \mathrm{~cm}$, and (c) $\mathrm{y}=4.0 \mathrm{~cm}^{y}=4.0 \mathrm{~cm} \underline{\text { Example } 19-5}$

Hey, this is question twenty eight point sixteen. We have a very long straight horizontal wire with it current, such that eight point two times ten to the eighteen electrons. Her second passed through any given point and that's going from west to east. So we are looking for the magnitude and direction of the magnetic field at a point four centimeters or point Oh, four meters directly above the weir. So the magnetic field from a long wire is shown here and noticed that the first thing we're gonna need to do is find the current. So the current is just going to be the number of elections passing through Per second time's the charge of the electrons. So there were no that there are eight point two times ten to meet eighteen electrons going through per second. So we're gonna want to multiply that by the tart of each individual electron, which is going to be one point six percent the minus nineteen cool ums. And when we played red in refined. But the current in this case is one point three one gramps. So now he were current and looking at our original creation up here, we have all the other constants. So all we need to do here is plug in one point three one for this plug an O point Oh, four to this, because you know the distance and that's going to give us a magnetic field with magnitude six point five six times ten to the minus six us. Now we're told that these currents are moving from west to east. But remember that electrons have a negative charge. So this means that currents as conventionally defined is actually going from east to west. And so imagine pointy or thumb from east to west of pointing left to find the direction of the magnetic field. We wanted a girl. Our fingers over s o up above four centimeters above this wire, our fingers are going to be pointing into the page which corresponds to a cardinal cardinal direction of north. So this magnetic field has magnitude six point five six times. Gentlemen, it's six. Tesla's pointing north

This problem covers the concept of the magnetic field produced by your current carrying. Why the magnetic field strength by the virus may not I upon to party and substitute the value. So B. Equals four by Into Tenders -7 islam meters. Point here. Into the current is yeah uh at MPO a bomb two pi into the distance from The wire is eight cm. We need to convert scenting with them to meet us. Therefore we have to multiply with 100 cm for meat. So the magnetic field magnitude is one and 2 Tenders -5 Tesla. Now we need to find the direction. So from the right hand call through if we hold the current carrying. Where in in our hand and point uh along the direction of the current gender direction of the coal will give the direction of the magnetic field at point B. And from that we can say the direction of the magnetic field at point please longer direction into the page. So we can say the magnetic field at P equals one into And his -5 Tesla into the peach

Hi. In the given problem there is a straight current getting wired of finite land. This is the observation point P. Two whose distance from one end of the wire Is given as R is equal to 25.1 centimetre lamp of this wire is given us Hell is equal to 13.6 centimetre. And the current passing through this wire is 0.693 ampere No, we have to find a magnetic field at this observation point to if this angle 5 1, let it be 5 1. And here angle made by this observation point at the other end at the right end of this wire will be zero degree. So first of all, we will find 5 1 to find this 5 1. We use this right angle triangle in which 1051 will be perpendicular upon base means this will be 13.6 centimetre divided by 25.1 centimetre. And it comes out to be 0.542. So 5 1 will be 10 Inverse 0.542, Which will come out to be 28.5°. So finally, magnetic field that point P two Will be given by biting seventh. Slum. You not by four pi into I buy art into sign 5 1 plus signed by two. Now plugging in all known values B is equal to 10 par -7 for immunity on four. by Into current, which is 0.693 Divided by distance are which is 25.1 into 10 for -2 into signed 5 1 which is signed of 28.5° Plus sine of zero degree. So finally here it comes out to be 1.32 into 10 for -7 Tesla. Or we can say this is 132 Nano Tesla, which is the answer for the given problem here. Thank you.

Hi in the given problem, there is Y axis which is shown vertically downward. Then there are the X and xerox is also here. This is the xerox is shown like this and this is the X axis supposed to be coming out perpendicular lee from that plane of paper here like this. So this is X axis. This is Xeroxes plus Z axis, this is plus X axis, This is plus why. And here this will be minus Y. And in finite length wire is placed along this Y axis which is carrying a current. I Having a magnitude of 8.00 ampere. There is a magnetic field, an external magnetic field along positive X axis which has given us be not Is equal to 1.50 Into 10 days. To the par -6 Tesla. No, we have to find that net magnetic field due to this wire and due to this external magnetic field does some of these two magnetic fields at various given points. So first of all, in the first part of the problem, the observation point is situated here at which X. is equal to zero and 0 has been given as 1.00 m means if we consider this to be the origin, The distance of observation point from this current carrying conductor is 1.0 m. So using bite and savage slot magnetic value to wire, B. W. Will be given by the expression new. Not by four pi Into two. I by our So plugging in Holland values. This is standard for -7. Tesla meter for MPO Into two into a time period divided by R. Which is 110 m. So finally here this magnetic field comes out to be 16 into 1084 -6. Best lock and using right hand thumb rule. Okay, the direction of this magnetic field is a long negative at sex is like this yep. So this is the W In first part of this problem. Yeah, we can mark it as part of it. So net magnetic will be equal to the difference of these two fields And as a b note is having a lesser magnitude as compared with this VW VW is 1.6 and be not was just 1.5. So net magnetic will will be B is equal to B W minus B. Not What you can say, this is 1.6 -1.5. Taking this standish 1 -6 Tesla as a comin out. So leaving behind it will be 0.1 into 10 for -6. Tesla. Or we can say this is 0.1 Micro Tesla answer for the first part of the problem. And this net magnetic field will be directed along the direction of BW means along negative X axis. We can write it here. So this is a long negative X Access. So this magnet will may also be written as -0.1 Micro Tesla. I get No in the 2nd part of the problem. The observation point now is here at X axis we can market as part B. So here This position of Zet has been given a zero and X has been given us 1.00 m. So if we find the magnitude of B W means magnetically due to while it will come out to be having same magnitude as the BW at the first point Doans this is 1.6 into 10 1 -6 Tesla. But using right and can rule the direction of this magnetic field will be towards means it will be a long positives and access like this. So here this is VW and this is be not. So in order to find their magnitude the resultant, you will have to apply vectors some here. So using vector cem As there is a 90° angle between them. The net magnetic will will be given by square toto square of VW's plus square of be not means plugging in or non values here. This is 1.6 into 10 dish par -6 Tesla to the whole square plus 1.5 into tended bar -6 square. So taking this tendency for -6 as a common out after making a square of it, it will come out to be tender 1 -12 Living inside this is 2.56 plus 2.25. And finally this is yeah, four point it won into tended bar minus 12. So finally the magnetosphere will come out to be 2.19 into 10 days par -6. Tesla. Or we can say B is equal to 2.19 might grow. S lock and if you find its direction for its direction. Mhm. Yeah this is the resultant magnetic field. If we consider this angle to beat it up, this theater angle will be given by Dante talk is equal to BW divided by B. Not. Yes, this is B W. The magnitude will do to wire divided there be not means this is 1.6 into 10 hr minus six, divided by 1.5 into 10 days for -6 which comes out to be 1.067. So finally Tita will be given by Then in verse of 1.06 or seven which comes out to be 46.9 degree. So the angle is 46.9 degree from positive X. Access to words positive zed exist. Answer for the second part of the problem. Finally, in the third part of the problem, we have to find magnetic will result in magnetic field at a point given here and now. The direction of this magnitude we're using right And thumb rule will be a long positive X axis. This will be D. W. This time distance here. This distance is just given a 0.25 m. So finding this VW now Which is given by the same expression for bite and seven slim. You know by 4.22 I by our means. This is standish 1 -7. multiplied by to into a time period divided by just 0.25. So here it comes out to be 6.4 into 10 HR -6 Tesla. Sonett magnetically. This time will be Given by addition of these two fields as BW is in the same direction as that of the not so physical too BW plus B. Not Then taking 10 days for -6 as a common out, it will be 6.4 plus 1.5 into 10 days par -6 Tesla. So finally we can save the is equal to 7.9 into tended bar -6 Tesla or Physical to 7.9 Micro Tesla. And this is directed along positive X excess. Answer for the third and the last part of the problem. Thank you.


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