Video Transcript
Parts (a), (b), (c), and (d) in the
diagram show a straight piece of copper wire moving through a magnetic field. The magnetic field is uniform, and
in each part the wire is moving at the same speed but in a different direction
through the magnetic field. Which of (a), (b), (c), and (d)
shows the motion of the wire that would lead to the greatest potential difference
being induced in it?
To answer this question, we need to
work out how the direction of the copper wire’s motion will affect the magnitude of
the potential difference that’s induced in the wire. Let’s start by clearing some room
on screen and thinking about how a potential difference can be induced across the
wire.
Imagine we have a straight piece of
copper wire. We can look at the wire from a
different angle, like this, so that the length of the wire is pointing into the
screen. Currently, there is no potential
difference between the two ends of the wire. The wire is not connected to a
circuit, and there is nothing else near the wire that could create a potential
difference.
Now let’s think about what would
happen if the wire was then placed into a uniform magnetic field. When the wire is stationary in the
magnetic field, there is still no potential difference between its two ends. But if the wire then started to
move through the magnetic field, it is possible that a potential difference could be
created across the wire.
Imagine that the wire begins to
move in this direction. We can see that, as the wire moves,
it will cross these magnetic field lines. When the wire moves in such a way
that it crosses magnetic field lines, a potential difference will be induced between
the two ends of the wire. This is electromagnetic
induction. The magnitude of the induced
potential difference is proportional to the rate at which the wire crosses the
magnetic field lines. Thus, if the wire crosses the field
lines at a greater rate, then a greater potential difference is induced.
Now this question is asking us to
identify the part of the diagram (a), (b), (c), or (d) that shows the motion of the
wire that will induce the greatest potential difference. So to answer this question, we need
to work out which diagram shows the wire that will cross the field lines at the
greatest rate. We were told that in each option,
the wire has the same speed. The only difference between each of
the diagrams is the direction that the wire is moving.
So how does the direction of the
wire affect the rate at which the wire crosses the magnetic field lines? To think about this, let’s return
to our example diagram. Imagine that the wire is moving
through the field at a constant speed for one second. Notice, too, that it’s moving
perpendicular to the magnetic field so that it crosses each field line at 90
degrees. Say that after one second, the wire
will have moved this distance and thus will have crossed three magnetic field
lines. So here, the wire crosses the
magnetic field lines at a rate of three lines per second.
Now imagine that the wire moves at
the same speed but in this direction so that it crosses each field line at an angle
that is not equal to 90 degrees. After one second, the wire will
have moved the same distance as before, but because the wire moved in this
direction, it only crosses these two field lines. So when the wire is moving in this
direction, it crosses the field lines at a rate of two per second.
Finally, now consider the wire
moving in this direction, parallel to the field lines. Notice that when the wire moves in
this direction, it will never cross any of the magnetic field lines. In other words, the wire crosses
the field lines at a rate of zero per second.
So we’ve seen that the wire crosses
the magnetic field lines at the highest rate when its direction of motion is
perpendicular to the field lines. This, therefore, corresponds to the
greatest possible potential difference being induced across the wire.
If we look at the diagram that was
given to us in the question, we can see that part (c) shows the wire crossing the
magnetic field lines at an angle of 90 degrees. In parts (a) and (b), the wire is
crossing the field lines at different, non-right angles. And in part (d), the wire is moving
antiparallel to the field lines and so is not crossing them at all. Thus, we know that part (c) of the
diagram shows the wire crossing the magnetic field lines at the highest rate.
Because the potential difference
induced across the wire is proportional to the rate at which the wire crosses the
magnetic field lines, part (c) shows the motion of the wire for which the greatest
potential difference is induced in it.
