A wire along the y-axis carries current in the +y-direction. An experimenter would like to arrange a second wire parallel to the first wire and crossing the x-axis at the coordinate $x=2.0\text{ m}$ so that the total magnetic field at the coordinate $x=1.0\text{ m}$ is zero. In what direction must the current flow in the second wire, assuming it is equal in magnitude to the current in the first wire? Explain.

Video Transcript

This is College Physics Answers with Shaun Dychko. A wire is positioned on the y-axis carrying current in the positive y-direction so it's going upwards and a second wire is located at x equals 2 and it's parallel to the first wire and the current direction has to be chosen such that the magnetic field at x equals 1 is 0. So what direction should the current be? And the currents are the same magnitude so that at this position, which is equidistant from both wires, the magnetic field strength will be the same for both wires but we need the directions to be opposite here. So if we consider this wire along the y-axis and figure out the direction of magnetic field it produces, we grab this wire with our right hand and the thumb has to point upwards and the fingers will curl in the direction of the magnetic field and at this position, the field will be into the page. So if I write B due to the first wire, that's an x directed into the page there but... let's just write an x. Okay! But if you consider this second wire here and do the right hand rule for it, and thumb pointing upwards and finger is when they curl around the wire once it gets to this position, the magnetic field is going to be pointing out of the page due to this wire and that's what we want, we want the fields to be in opposite direction and that happens when this current is upwards as well.