Video Transcript
A long straight wire is carrying a
constant current 𝐼 that induces a magnetic field 𝐵. Magnetic field lines of 𝐵 are
shown in the diagram. Based on the diagram, state the
direction of the conventional current in the wire.
Okay, so here’s our wire, which we
know is carrying a constant current. But we don’t yet know the direction
of current in the wire. Since it’s oriented vertically, it
could either be from bottom to top or top to bottom. Now we know that the current
induces a magnetic field as represented by the field lines in the diagram. And when viewed from above, these
field lines point in the clockwise direction. Interestingly, this is all the
information we need to determine the direction of current in the wire. Let’s recall the right-hand rule
for the magnetic field due to a current in a straight wire like we have here.
Using the right hand, of course, if
we point the thumb in the direction of current and then wrap our fingers around the
wire as if we’re grabbing it, then the direction that the fingers curl in
corresponds to the direction of the magnetic field. It’s okay that we don’t know the
direction of current because we do know the direction of the magnetic field. Let’s try it out. Using our right hand, let’s go to
grab the wire, making sure the fingers curl along the direction of the magnetic
field. So with the fingers curling
clockwise as viewed from above, notice that the thumb has to be pointing down. This tells us that the direction of
current in the wire is from top to bottom.
Just to double-check though, we can
see what happens if we grab the wire the other way with the right thumb pointing
up. If the current was in this
direction, bottom to top, that would mean the magnetic field lines have to go the
opposite way, counterclockwise as viewed from above. But looking at the field lines in
our diagram, we know that this is not the case, so we can be extra sure in our
answer. Here, the direction of the
conventional current in the wire is top to bottom.
