Video Transcript
Several horizontal pairs of
parallel conducting wires are stacked vertically. The magnitude of the current in
each wire is the same. A cross section of the resultant
magnetic field due to the currents is shown in the diagram. Which of the configurations of
current directions shown would produce the resultant magnetic field?
In this question, we are given a
cross section of a magnetic field. We need to work out which of the
configurations of current directions would produce this resultant magnetic
field.
To begin, we will recall how the
direction of the magnetic field is determined by the direction of the current that
produces it. We can do this using the right-hand
grip rule. Pointing the thumb of our right
hand in the direction of the current, our fingers curl closed in the direction of
the magnetic field. So for a current pointing out of a
cleared space on the screen, the magnetic field looks like this. And for a current pointing into the
screen, the magnetic field would look like this.
Now if we consider two
current-carrying wires that are parallel to each other, we can construct the net
magnetic field created by these two currents. For two currents which are pointing
in opposite directions, we get a net magnetic field that looks like this. In this scenario, there is a high
density of field lines in the vertical line midway between the pair of
current-carrying wires. This indicates a strong magnetic
field in the middle of these two wires. We can also notice that most of
these field lines are vertical or close to being vertical.
For two currents which are pointing
in the same direction, we get a net magnetic field that looks like this. In this scenario, the magnetic
field directly between the two wires is zero, and the field in that general area is
weak. Again, we can draw a vertical line
midway between the wires. We see that the field lines are
close to being horizontal when they cross this line.
Now let’s study the magnetic field
diagram given to us in the question. If we consider a vertical line
midway between each horizontal pair of current-carrying wires, we see that there are
very few field lines that exist along this line. Most of the field lines are close
to being horizontal when they cross this line. This suggests that this net
magnetic field corresponds to pairs of parallel conducting wires with currents that
are pointing in the same direction.
As can be seen in the answer
options, only one option contains pairs of parallel conducting wires with currents
that are pointing in the same direction. This is option (II). Therefore, the configuration of
current directions shown which would produce the resultant magnetic field is option
(II).
