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. (A) The same as, (B) opposite to,
(C) at a right angle to.
In our diagram, we see this
current-carrying wire. Because the wire runs into and out
of the screen, it can only carry current either into or out of the screen. This current, like all currents,
creates a magnetic field around itself. The arrow shows us the direction of
that field at this point called point 𝑃.
In general, the direction of the
magnetic field created by a current in a straight line is given by what’s called a
right-hand rule. If we have a wire and that wire
carries a current, we’ll call it 𝐼, then we can use our right hand to determine the
direction of the magnetic field created by this current. We point our right thumb in the
current direction. Then, we curl the fingers on this
hand closed. The direction that our fingers curl
is the direction of the magnetic field around the wire. That is, the magnetic field created
by this current points in circles like this around the wire.
We can use the same right-hand rule
along with our knowledge of the magnetic field direction at point 𝑃 to determine
the magnetic field direction at point 𝑄. Recall that the current in this
wire can either point into the screen like this or out of the screen like this. If the current does point into the
screen, then according to our right-hand rule, we would point the thumb on our right
hand in that same direction into the screen. And then curling our fingers, they
would curl in a clockwise direction. This would mean that at point 𝑃,
the magnetic field from the current would point downward. We know, however, that this is not
the case that it points opposite to this direction, and therefore the current in the
wire cannot point into the screen. That means it must point out of the
screen.
Pointing the thumb on our right
hand in that direction, our fingers curl counterclockwise. That would mean that at point 𝑃, a
point directly to the right of the wire, the magnetic field would indeed point
upward. But then at a point exactly to the
left of the wire, as point 𝑄 is, the counterclockwise direction relative to the
wire would mean that the field points downward. This tells us how we can correctly
fill in the blank of our sentence. We choose answer choice (B) so that
our sentence now reads “The direction of the magnetic field at point 𝑄 is opposite
to the direction of the field at point 𝑃.”
