A solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius b and outer radius c (Fig. E28.43). The central conductor and tube carry equal currents I in opposite directions. The currents are distributed uniformly over the cross sections of each conductor. Derive an expression for the magnitude of the magnetic field (b) at points outside the tube (r > c).

Video transcript

Hey everyone. So this video, we are working with magnetic fields. Let's see what they're giving us and what they're asking from us. We know we have a long cylindrical aluminum rod and it's surrounded by a copper cylindrical shell. The two conductors are separated by an electrical insulator. The rod and the shell carry equal and opposite currents. That's an important thing to note here of a given magnitude that are distributed uniformly determine the magnitude of the magnetic field at a point located at some distance R. That is outside um are to the axle of the rod. So the first thing we need to do is recall amperes Law when R is greater than are too NPR's law can be written as B equals and you not I over two pi r. So um let's just draw kind of what's going on here. We have one aluminum rod and that's got a charge I and it's surrounded by this shell and that has a charge will call this one negative I um it doesn't really matter which is positive or negative. We just know that they are equal and opposite. Okay, so this I turn here is really the sum of the currents in the system and we know from the information that i is equal to one positive I and minus I. And so that is equal to zero because they're equal and opposite. So when this term goes to zero, the entire term for B, the magnetic field, the magnitude of magnetic field goes to zero and that's our answer. That's all for this problem. Um And so we look at our possible answers. That's answer. A and that's it. We'll see you in the next video.