As a new electrical technician, you are designing a large solenoid to produce a uniform 0.150-T magnetic field near the center of the solenoid. You have enough wire for 4000 circular turns. This solenoid must be 55.0 cm long and 2.80 cm in diameter. What current will you need to produce the necessary field?

Video transcript

Hey, everyone. So in this problem, we are working with magnetic fields, let's see what they give us. And what they're asking for us, there is a tightly warm coil, they give us the length and the radius and they say that the coil has 2500 turns. We are asked to generate a magnetic field of a specific strength at the center of the solenoid boil. And they um are asking us to calculate the current in that in the terms to generate that magnetic field. So this is a pretty straightforward plug and chud kind of question as long as we first remember the um formula for magnetic fields in terms of current. So let's recall that that is given as B equals mu not N over L times I so B is our magnetic field. So let's take this turn by turn, we are given the magnetic field strength here that 0.34 teslas, we can recall that mu knot is the permeability of free space. It's a constant that is four pi times 10 to the minus seven tesla meters for amps. We have N is our number of turns. That was also given to us in the problem. It's 2500 and then L is the um length of the coil that was given to us as 85 centimeters. I'm just gonna rewrite that here as 0.85 m. So from there, all we have to do is rearrange this equation in terms of I or current and solve it out. So that becomes I equals el over UK NOTT N plug in everything from there. So 0.34 Teslas times 0.85 m over Muno four by 10 to the minus seven Tesla meters or amps and times are turns 2500. We can even see that our units here work out. It's very clean, straightforward plug that into our calculator. 92.0 amps. Look at our possible answers and the correct answer is D 92 amps. That's all we have for this problem. We'll see you in the next video.