Video Transcript
The diagram shows a long straight
wire that carries a current 𝐼. As a result, a magnetic field that
is far stronger than Earth’s magnetic field can be measured at point 𝑃, which is a
short distance away from the wire. If a small compass is placed at
point 𝑃 with its face pointing in the opposite direction to the current, which
direction will the needle point? (A) Right, (B) left, (C) into the
screen, or (D) out of the screen.
These answer options show four
different ways that the compass needle can point. And note that although the needle
has a symmetric shape, the red side is considered the true point of the needle. Now, we might recall that a compass
typically guides us by using Earth’s magnetic field. But we’ve been told that the
magnetic field produced by the wire is far stronger than Earth’s. This just means that we should
disregard any magnetic field that isn’t produced by this current-carrying wire.
So then, how do you know which
direction the needle will point? Well, imagine that we had a uniform
magnetic field like this. Here is what it would look like if
we placed the compass in the middle of this field. Or if the field pointed in the
opposite direction, the compass would look like this. This shows us that the needle will
point in the direction of the magnetic field, as represented by the field lines we
drew here in pink.
So, returning to this question, to
determine which way the needle will point if the compass is placed at point 𝑃, we
need to determine which direction the magnetic field itself points there. Note that the compass is placed at
point 𝑃 with its face pointing in the opposite direction of the current in the
wire. So the compass is facing up. Since the needle will point in the
direction of the magnetic field, answer option (A) suggests that the field at point
𝑃 points to the right. (B) says that the field points
left, (C) says that the field points into the screen, and (D) says out of the
screen.
Now, let’s clear some room on
screen, but we’ll make a note to remember that the compass is placed face up at
point 𝑃. Next, to determine the direction of
the magnetic field there, let’s recall the right-hand rule for the magnetic field
due to a current in a straight wire, like we have here. The rule says that using the right
hand, if we point the thumb in the direction of the current and curl the fingers
around the axis of the wire as if we’re grabbing it, then the direction that the
fingers curl around the wire corresponds to the direction of the magnetic field.
Let’s try it now. If we were to grab the wire with
the right thumb pointing down, it would look like this. Notice that because the fingers are
curling around the wire, on the left side, the fingers are pointing into the
screen. But on the right side of the wire,
where point 𝑃 is, the fingers point out of the screen. Therefore, at point 𝑃, the
magnetic field points out of the screen. And since we’ve already determined
that the compass needle will point in the same direction as the magnetic field, we
know that the needle will point out of the screen as well. Therefore, option (D) is
correct. If a small compass is placed face
up at point 𝑃, the needle will point out of the screen.
