The diagram shows a section of wire
that has been positioned parallel to a uniform 0.1-tesla magnetic field. The wire carries a current of two
amperes. What is the direction of the force
acting on the wire due to the magnetic field?
Okay, in this diagram, we see this
section of wire here, which is parallel to a uniform magnetic field. The diagram also shows us that
charge in the wire moves left to right. Based on this, we want to solve for
the direction of the force that acts on this wire due to the magnetic field. Now, we have to be a bit careful
here. Seeing that we have a
current-carrying wire in a magnetic field, we might think of the mathematical
relation for the force on such a wire.
That equation says that this force
is equal to the strength of the magnetic field multiplied by the current magnitude
in the wire times the length of the wire exposed to the field. But there’s an important condition
that’s required in order for this equation to be valid. The condition is that the magnetic
field direction is perpendicular to the direction of current in the wire. In our case though, we can see that
condition is not met because the current and the magnetic field point parallel to
one another. When this is the case, this
equation here for magnetic force doesn’t apply. And, in fact, the magnetic force
experienced by this current-carrying segment of wire is zero when the current and
magnetic field are parallel. In other words, the force acting on
this section of wire is zero.
Now, we’re not asked about the
force magnitude itself, but rather its direction. We can see though that this
realization impacts our answer to the force direction. That’s because a force of zero has
no direction to it. So our answer to this question can
simply be that there is no force acting on the wire. Since there’s no force, there’s no
direction. And this then is our answer.