Video Transcript
The diagram below shows a cross
section of a current-carrying wire. The magenta arrow shows the
direction of the magnetic field at point 𝑃. Fill in the blank. The direction of the magnetic field
at point 𝑄 is blank the direction of the field at point 𝑃. We’ve got three options to choose
from. (A) At a right angle to, (B)
opposite to, or (C) the same as.
So, in this question, we’re shown a
diagram of a cross section of a wire, which is carrying a current, as well as two
points labeled 𝑃 and 𝑄. We can also see a magenta, or pink,
arrow here that shows us the direction of the magnetic field at point 𝑃. We’re being asked to work out the
direction of the magnetic field at point 𝑄.
Now, in order to figure this out,
we can start by recalling that when a wire carries a current, a magnetic field is
created around the wire. The magnetic field produced is
always perpendicular to the direction of the current, which means that the magnetic
field around a current-carrying wire will wrap around the wire, like this.
Now, the direction of this field
can either be clockwise or counterclockwise. This depends on the direction of
the current in the wire. Fortunately, there’s an easy way to
figure out the direction of the magnetic field if we know the direction of the
current. And this is known as the right-hand
rule. If we extend the thumb of our right
hand and point it in the direction of a current, then our fingers will curl in the
direction that the magnetic field is oriented.
Now, in this diagram, we’re looking
at a cross section of a wire. This means that the current it
carries must either be going into the screen or out of the screen. We can use the right-hand rule to
see what happens in each case.
If the current were going into the
page, which we can signify with a cross, then we can work out the direction of the
magnetic field that would be created by pointing the thumb of our right hand into
the screen. Doing this, we find that our
fingers curl in a clockwise direction. This means that the magnetic field
around the wire would go in a clockwise direction, too.
However, if we look carefully at
the diagram, we can see that this conflicts with the information we’ve been
given. If the field went around the wire
in a clockwise direction, then the magnetic field at point 𝑃 would point downward,
not upward. This means that the current in the
wire can’t be directed into the screen.
So how about if the current was
directed out of the screen? We can represent this in our
diagram by replacing our cross with a dot, like this. Applying the right-hand rule to
this current, we point our right thumb out of the screen. Doing this, we find that this time
our fingers curl counterclockwise. This means that the magnetic field
around the wire will be oriented in a counterclockwise direction if the current is
directed out of the screen. We can see that this fits with the
fact that the magnetic field at point 𝑃 is pointing upward. So we know that in this scenario,
the wire must be carrying a current out of the screen.
We can also see that because point
𝑄 is located to the right of the wire, the magnetic field at this point must also
be pointing upward. And that’s the same direction as at
point 𝑃. So our final answer is option
(C). The direction of the magnetic field
at point 𝑄 must be the same as the direction of the magnetic field at point 𝑃.
