### Video Transcript

The diagram below shows the field lines of the magnetic field produced by a wire carrying a current into the screen. At which of the labeled points on the diagram is the magnetic field weakest?

In our diagram, the current pointing into the screen is represented by this yellow dot. Around this dot, we see the concentric rings representing magnetic field lines. Scattered among these field lines are five labeled points. Here’s point i. Here’s point ii, point iii, point iv, and point v. We want to identify at which of these five points the magnetic field strength is weakest.

We can begin by remembering that for the magnetic field created by a current-carrying wire, like we have here, the strength of that magnetic field 𝐵 is proportional to one over the radial distance from the wire. That is, the radial distance will be measured along a line like this. Based on this relationship, the smaller the value of 𝑟, the larger the magnitude of 𝐵. This tells us that the closer we get to our current-carrying wire, the stronger the magnetic field. And then, conversely, the farther away we get, the weaker the field is.

So then, whichever of our five labeled points is farthest away from the current-carrying wire is the one that will label the weakest magnetic field of the five spots. We see that point i is closest to the wire. Point ii is the next closest. Point iii is the next closest, then iv, and then finally point v. Since point five is farthest away, this point of the five labels the location of the weakest magnetic field. Our answer is point v.