Video Transcript
A circular loop of wire is carrying
a constant current 𝐼 that produces a magnetic field. The loop intersects a flat plane at
points 𝑃 and 𝑅. The wire is normal to the plane at
the points of intersection. A small compass is placed in the
plane at the center of the loop of wire, 𝑄, with its face pointing upward. In which direction will the needle
of the compass point? (A) Right, (B) left, (C) out of the
screen, or (D) into the screen.
Here we have a loop of
current-carrying wire that’s producing a magnetic field. And we want to consider placing a
compass face-up at the center of the loop. To answer this question, it’ll be
helpful to know that in the presence of a magnetic field, a compass needle will
point in the direction of the field. So in order to determine which way
the needle will point when the compass is placed at the center of the loop of wire,
we need to determine which direction the magnetic field points there.
Recall that the direction of the
magnetic field depends on the direction of the flow of charge through the wire loop
and that we can use the right-hand screw rule to help us determine the direction of
the magnetic field. To do this, remember that a
right-handed screw can only be turned in one direction to drive it into a
surface. So if the direction we must turn
the screw in corresponds to the direction of the current in the loop, then the
direction that the screw points, the direction it is being driven in, is the
direction of the magnetic field at the center of that loop.
In the diagram, we see that the
direction of charge flow in the loop points counterclockwise. We cannot tighten the right-handed
screw in this way. So we have to turn the screw around
so that it’s pointing out of the screen towards us. This means that the magnetic field
at the center of the loop points out of the screen. And since we know that the compass
needle will point in the same direction as the magnetic field, we know that answer
choice (C) is correct. The compass needle points out of
the screen.
