A solenoid is designed to produce a magnetic field of 0.0270 T at its center. It has radius 1.40 cm and length 40.0 cm, and the wire can carry a maximum current of 12.0 A. (b) What total length of wire is required?

Video transcript

Welcome back everybody. We are tasked with manufacturing a solenoid. With a couple of conditions. We are told that it must generate a magnetic field of 0.15 Zero Tesla's we're told also that it must have a diameter of two cm or .02 m. We're told that it must have a minimum length of centimeters or 500.5 m. And that a current of 60 amps will be able to run through it. Now we are tasked with finding what the total length of the conductor wire will be needed to generate this magnetic field. Lucky, luckily we have a formula for this. We have that the length is going to be equal to the number of turns, times two pi times the radius of each turn. But we have the radius just by dividing the diameter in half. But we need to figure out what this value is right here. So what we can do is look at the formula for the magnitude of a magnetic field. We have another magnetic field is equal to mu not times our N over L times our current. Now this L just to to be very clear here is our minimum length that we need. So let's go ahead and do this. I am going to divide both sides by mu not and I mu not and I and then we get that N over L. S. Is equal to our magnetic field divided by mu not times our current. So let's go ahead and calculate this then. So we have N over L. S. Is equal to 0.15 divided by four pi. Times 10 to the negative, seventh times 60 amps. This gives us 190 now remember however we need this end so we gotta multiply both sides by this L. S. So L. S. This cancels out on this side and we get on the right side times L. S. Which is just the same thing as 1990 times 0.5. Giving us an end value of 995 turns great. Now that we have found that we are ready to find the total length of our conducting wire needed to generate the solenoid and the magnetic field we have L. Is equal to using this formula up here. 995 times two pi times our diameter divided by two. Which will give us the radius. And when you plug this into our calculator we get a final answer of m of coil corresponding to answer choice. D Thank you all so much for watching. Hope this video helped. We will see you all in the next one