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 strongest?
In our diagram, the yellow dot at
the center represents the wire carrying current into the screen. Around this, we see a series of
concentric circles with arrows on the circles. These are magnetic field lines
created by the current. And we see that, overall, this
magnetic field points clockwise around the wire. What we want to work out, though,
is at which of the label points on the diagram — and there are five such points,
point i, point ii, point iii, point iv, and point v — is the magnetic field
strongest?
We can recall a connection between
magnetic field strength and magnetic field line density. Specifically, the more dense
magnetic field lines are, the stronger the field is in that region. In the case of our diagram, say
that we had a box of some fixed size. And we moved this box to different
locations around our current-carrying wire. The more magnetic field lines we
would see inside the box, the stronger the magnetic field in that region. So, for example, when the box is
farther from the wire out here, there are fewer magnetic field lines contained
within this volume than when the box is close to the wire like it is here. We can say then that the magnetic
field is stronger in this region than it is in this region.
The overall conclusion we can draw
is that the closer we get to the wire, the stronger the magnetic field. Indeed, we notice that if we start
at a point far away from the wire and then move in close to the wire, the magnetic
field lines become more and more closely spaced together. This is a sign that the magnetic
field strength is increasing. So then whichever of our five
points is closest to the wire, that point will indicate the location of the
strongest magnetic field.
Point v out here is farthest from
the wire. Next, we have point iv, then point
iii, then point ii is closer, but point i is closest of all. Of all our labeled points then,
this one indicates the location of the strongest magnetic field. Notice, by the way, that if we had
another point that was the same distance from the wire as point i, the magnetic
field strength would be the same magnitude there. In this case, though, since we’re
only considering our five labeled points, we give our answer as point i.
