Question Video: Determining the Direction of the Magnetic Field at a Point near a Current-Carrying Wire Physics

Video Transcript

The diagram shows a long, straight, horizontal wire that carries a current 𝐼. As a result of the current, a magnetic field is produced, which is measured at point P. The point P is in the plane of the wire, a short perpendicular distance from the wire. What is the direction of the magnetic field at point P?

In our diagram, we see this long, straight wire carrying a current 𝐼. And then what we’re told is a short, perpendicular distance from the wire is this point marked point P. Now, because this wire carries a current, we know it will produce a magnetic field around itself. This field extends arbitrarily far away from the axis of the wire, which means that this point P right here will experience it.

In this question though, we’re not interested in the strength of that field at point P, but rather its direction. And when we’re talking about the direction of the magnetic field produced by a long current-carrying wire, we can remember that we can figure this out using what’s called a right-hand rule. When we use this rule, we take our right hand and we imagine positioning it so we’re almost grasping on to this current-carrying wire. Next, we point our thumb in the direction of the current in the wire. And we then curl our fingers around this imaginary wire axis. When we do this, the direction that our fingers curl indicates the direction of the magnetic field around this wire.

Note that the way we’ve been talking about this right-hand rule aligns with the way that our wire is oriented in this exercise. The wire is aligned left to right. And the current in it points to the right, which means that this application of the right-hand rule we just saw answers the question for us of which way the magnetic field around this current-carrying wire points. That field will exist in concentric circles, and we’ve just drawn a very few of those loops here around our wire. This means that if we were to draw a magnetic field line centered on our current-carrying wire and passing through point P, that line would look something like this.

Now, just to see this from a different perspective, imagine that we put our eye here in relation to our current-carrying wire. If we did that, we would see the wire end on looking something like this. And say that in relation to the wire’s axis, point P was right here. What we’ve seen from applying this right-hand rule is that the field line move like this through that point.

Now, for the sake of our answer to this question, it’s important to consider our perspective with the original diagram. That is, in what direction does the magnetic field move through point P looking at the wire this way? We can see that, from this perspective, the magnetic field line moves into the screen at this point. And so that’s our answer. The direction of the magnetic field at point P is into the screen.