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.
