Video Transcript
Fill in the blank. A wire of length 120 centimeters
moves perpendicularly to a magnetic flux of density 0.6 teslas. If the wire experiences an emf
between its ends of two volts, then the wire is moving with a velocity of blank
meters per second. Is it (A) 0.03, (B) 0.36, (C) 1.44,
or (D) 2.78?
Before we start solving this
problem, it’s worth noting that in this context we can take magnetic flux density,
which we measure in teslas as usual, to mean the same thing as magnetic field
strength. Also, we’ll assume that the
magnetic field in question is uniform. So let’s draw a diagram to help
visualize this.
We don’t know the precise direction
of the magnetic field, so let’s just choose to draw it pointing from left to
right. We do know that the length of wire
is moving in a direction perpendicular to the magnetic field. So let’s choose to draw it moving
downwards, noting that its direction of motion makes a right angle with the
direction of the magnetic field.
At this point, we should recall
that for a straight conductor moving through a uniform magnetic field, an
electromotive force, or emf, of magnitude 𝑙𝑣𝐵 sin 𝜃 is induced across it, where
𝑙 is the length of the conductor. 𝑣 is its velocity. 𝐵 is the magnetic field. And 𝜃 is the angle between the
velocity and the magnetic field.
We’ve been asked for the velocity
of the wire, so let’s rearrange this equation to make 𝑣 the subject. To do this, we can divide both
sides of the equation by 𝑙, 𝐵, and sin 𝜃. So those terms cancel out of the
right-hand side, leaving 𝑣 by itself. Thus, the expression can be written
as the velocity equals the induced emf divided by 𝑙𝐵 sin 𝜃.
Next, we should make sure that all
of our known values have the appropriate SI or SI-derived units. The emf is given as two volts, so
it’s good to go, and so is the magnetic flux density written as 0.6 teslas. And of course, 𝜃 is just expressed
in angular units. And here, 𝜃 equals 90 degrees. The only units that need to be
converted are centimeters for the length of the wire, which should be written in
plain meters. We know that one centimeter is one
hundredth of a meter, so 120 centimeters is equal to 1.20 meters.
Finally, we can substitute all
these values into the equation for velocity. Since all the values on the
right-hand side are expressed in appropriate units, we know that this formula will
give us a velocity value in the proper units of meters per second.
Now, entering this into our
calculator, we get a result of 2.777 and so on meters per second. And choosing to round to two
decimal places, this becomes 2.78 meters per second. This corresponds to answer option
(D), which is the correct answer. A wire of length 120 centimeters
moves perpendicularly to a magnetic flux of density 0.6 teslas. If the wire experiences an emf
between its ends of two volts, then the wire is moving with a velocity of 2.78
meters per second.
