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. (a) What minimum number of turns per unit length must the solenoid have?

Video transcript

Welcome back everybody. We are studying a wound coil that is intended to generate a magnetic field that has a magnitude of 0.63 Tesla. We are also told that it should be able to carry a maximum current of 20 amps and we are tasked with finding what the minimum number of turns is per unit length needed in order to carry that maximum current. Now I'm going to denote this N over L. Just down to a single variable of a lower case N. And this is exactly what we need to find. So let's look at the equation for the magnitude of a magnetic field that B is equal to mu not times N over L. Times our current this is equal to mu naught times little end times our current. And we have all of these values but we need to first isolate this end term right here. So I'm gonna divide both sides by mu naught times I you'll see that the terms cancel out on the right side and then we are left with that. The number of terms per unit length of time is equal to the magnitude of the magnetic field divided by mu not times our current. So let's go ahead and plug in our values. We have that our little N. Is equal to 0.63 divided by mu naught which is four pi times 10 to the negative seventh times 20 amps. Giving us a final answer of 2507 turns per meter which corresponds to our final answer. Choice of C. Thank you all so much for watching Hope. This video helped. We will see you all in the next one.