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.