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You wlsh coileineconstructsolenold with diameter of 2,00 cm that will produce magnetic fleld , 3.00 Tat Its center hen current 16,0 passing through the colls, You w...

Question

You wlsh coileineconstructsolenold with diameter of 2,00 cm that will produce magnetic fleld , 3.00 Tat Its center hen current 16,0 passing through the colls, You want the resistance The resistivity the wire usedi 1.70 (at 20.0PC), and You usng wire that has Cross sectiona Ofed of 3.14 m2. (Note that this solenoid may not necessarily tightly wound that the adjacent loops of wire wIll touch each other Nonetheless, Vou May assume that behaves Iilke a ideal salenai Determine the followlng nuMLer of

You wlsh coileine construct solenold with diameter of 2,00 cm that will produce magnetic fleld , 3.00 Tat Its center hen current 16,0 passing through the colls, You want the resistance The resistivity the wire usedi 1.70 (at 20.0PC), and You usng wire that has Cross sectiona Ofed of 3.14 m2. (Note that this solenoid may not necessarily tightly wound that the adjacent loops of wire wIll touch each other Nonetheless, Vou May assume that behaves Iilke a ideal salenai Determine the followlng nuMLer of turns needed on the solenoid 154 /4 Furns (b) length_ the solenoid



Answers

A solenoid is formed by winding 25.0 $\mathrm{m}$ of insulated silver wire around a hollow cylinder. The turns are wound as closely as possible without overlapping, and the insulating coat on the wire is negligibly thin. When the solenoid is connected to an ideal (no internal resistance) $3.00-\mathrm{V}$ battery, the magnitude of the magnetic field inside the solenoid is found to be $6.48 \times 10^{-3} \mathrm{T}$ . Determine the radius of the wire. $(\text {Hint:$ Because the solenoid is closely coiled, the number of turns per unit length depends on the radius of the wire.)

So for this problem, first will consider wrestle. Annoyed we for 100 transfer meter on a radius of 1.27 centimeters. Right, ASA, 0.127 meters on your interests. Illinois is Boeing 776 years after finding negative religious center, This is the usual equation for Selena magnetic field months and made zero number of turns, premier and passenger and I. It's hard a feel off for Europe. 00.468 desolate at the center of the solar. Now give it this fuel when we want to do. Now, if we want a long straight wire to generate the same my dick feel it's a solenoid at a distance off 0.127 meters. So we're gonna do is we're gonna take okay, Would you take this equation 14 people, So make it equal to the question for the magnetic field off a wire on the what did you want to find out his boat? All I W, which is used a current kid body wire the museum's cancel out and we can solve our I w I find that I don't leave the current in the wire He's two pi times the number of turns per meter and fastidiousness. Our has to current up the solar height, and they have sought out wire current off 297 appears.

Hi in this given problem, length of the solid night That has given us L is equal to 40 centimetre. Or It can also be given a 0.40 m. Its area of cross section. That is given as 8.0 centimetres square. Or in MTs system it will be 810 into tended bar minus form eatery Squire. The motor turns in this solenoid Are given as 300 And current passing through the solenoid is 1.2 M. Pierre. Then for iron core within this solenoid permeability is given us relative permeability. That is given us 600 new art. So in the first part of the problem, magnetic field induced within the core material that will be given by new and I. Where this new will be equal to new. Are into mu Not into N for end. This is the number of times per unit land means and by L into I For new art, this is 600 Into Mu not which is four by into 10 days par -7. Tesla m per ampere total turns 300. Land Lent is given a 0.40 m. And current passing through the solenoid is one point where I'm here. Now cancelling ampere with the ampere meter with the meter. Finally, this magnetic will induced within the core material comes out to be 0.68 Tesla which is the answer for the first part of this problem. Now, in the second part of the problem we have to find magnetic flux linked through the soil which will be given as five is equal to be dot A. So here it will be as a magnetic field is perpendicular to the area, so it will be parallel to the area vector. So it may be given as be a cost 0° For b. This is 0.68 Tesla for area, that is eight In 210 for -4 m square. So finally phillips here comes out to be 5.44 In 2, 10 days to the power minus for Weber. Or we can say this is 544 into 10 days 4 -6. Weber which finally made billionaires 544 micro vespa, which is the flux linked through the khoi. And that is the answer for the second part of this problem. Thank you.

This problem, we're gonna need it to important equations. First is the resistance for Solyndra conductor, it's row the restive ity temps l divided by a cross sectional area. We're also going to need the equation for the magnetic field from Selena. Just you, Not times and I tried to buy else where n is the total number of coils and l is the length now in part A will want to find the number of turns and that are required to generate the magnetic field Rather that that the problem is telling us is this in the solenoid? And so if you want a model LaSalle annoyed a side view, you can picture it as a bunch of wires with currents going into the page is labelled exes and another line of wires. All going out of them were with currents all going out of the page. So with the actual coils of the solenoid going between them Now, if we want to find the resistance from sewn in which we're gonna need to find the total number of turns, we're gonna use that equation from above and weaken. Rearrange that to solve for l the total length of our wire, which you can also see, is in our equation for the final solid. So when we rearrange, we find that l is equal to our times. Tire squared where r is the radius of the wire divided by row are restive et When we plug all of our values in we find the we get 5 57.7 meters. So that's our total length, and the number of turns that we have in our still annoyed is equal to the length of the wire divided by the circumference of the song lead. It is only basically just a bunch of circles that are coiled together, So we then get our length that we just found divided by two pi r off the song would. So we're gonna plug in our result from earlier or 57.7 divided by to pull two pi times 0.1 meters. Would you let out? We get a result of 919 total turns in our cell. Annoyed that are needed to sustain the magnetic field. Part B asked us to find the required length else all annoyed off our above or someone would so we're going to use that equation earlier for the magnetic field and we arranged to sell for our total length we found we know or be from the set of the problem. We just found the number of turns and we know the current that is going through a solemnly so all that's left is to plug in those quantities and then solved to fine.

For this question. We want to have a soul. Annoyed with the resistance are five homes that produces a magnetic field, be of four times. Sentiment is to test let at its center with the current I of four amperes. We're told that this Illinois is constructed from copper wire and copper wire wire has resisted V. I call roasted sea of 1.72 times, 10 to the minus eight homes per meter. The radius of this Illinois is one centimeter, which I convert two meters 20.1 meters, and we're told that the copper wire has a diameter of five millimeters. So I call our subsea the radius of the copper wire, which is half of that, which is 0.25 times 10 to minus three meters for part A. It says it wants to calculate in, which would be the number of turns in the wires that's needed. Okay, so to do that first we need to figure out the length of the wire that's needed, So we'll call this length of the copper wire Capital L. This is equal to the resistance. Are times the area of the wire a divided by three sensitivity grow subsea. Well, if we treat the wire as ah spherical, this is gonna be our multiplied by pi. Times are some c squared divided by the recent vivid receptivity Rose. Um, see. Okay, so now we can go ahead and plug our values, uh, into this expression when we find that this is equal to about 57 meters. So using that we can now determine the number of turns in since in here is equal to the total length l divided by two pi times the radius of the solenoid arsonists. Since that would be Mr Comforts. So plugging those values and we find that this is we're gonna round up because you could only have injector values of the number of turns. So we find that this is about equal to 908 turns mean boxes in Is your solution for part A Part B says to find the length of the solenoid. Um, so to do that first, we need to find the number of turns in this Illinois per unit length. We can get that from the fact that the magnetic field B is equal to Munich times, in which is the number of turned for unit length times the current high Rearranging this to sulfur and find that in here is equal to be divided by you, not times I you not as four pi times 10 to the minus sentence. We plug these values and when we find the number of turns is about seven 0.961 times 10 to the third Mrs turns per meter. Yes. And now that we know that we can find the length of the soul annoyed, I'll call that little l Mr just simply equal to Biggin divided by little. And the units have turns cancel on. We're left with units of meters and this gives us 11.4 times 10 to the minus two meters or 11 11.4 centimeters. Weaken boxes in his air solution for part B.


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