Video Transcript
When positioned at 90 degrees to a
magnetic field, a wire of length one meter carrying a current of four amperes
experiences a force of 0.2 newtons. What is the strength of the
magnetic field?
All right, so in this example, we
have a length of wire. This length is one meter long. And we’re also told that the wire
carries a current of four amperes. And then, in addition to this, this
current-carrying wire is positioned at 90 degrees to a magnetic field. So we could draw magnetic field
lines that look like this, where these lines, as we’re told in the problem
statement, are perpendicular to our wire. For our purposes, whether the field
lines point straight up as we’ve drawn them or if they pointed straight down doesn’t
make a difference so long as the field lines are at 90 degrees to our wire.
We’re told that, in this magnetic
field, our wire experiences a force, and it has a magnitude of 0.2 newtons. Knowing all this, we want to solve
for the strength of the magnetic field that the current-carrying wire is in. We can call that magnetic field
strength capital 𝐵. And let’s say that the force the
wire experiences in the field at 0.2 newtons is 𝐹 sub 𝐵. So we have all this information,
but we need some way to tie it all together. We can do this by recalling a
mathematical expression for the magnetic force experienced by a current-carrying
wire in a magnetic field. That force is equal to the strength
of the magnetic field 𝐵 times the magnitude of the current running through the wire
multiplied by the length of wire exposed to the magnetic field.
Now, in our case, it’s not 𝐹 sub
𝐵 we want to solve for, but rather the magnetic field strength 𝐵. So to rearrange and solve for that,
let’s divide both sides of the equation by 𝐼 times 𝐿 causing those two terms to
cancel out on the right-hand side. So then, the magnetic field is
equal to the magnetic force divided by the current times the length of the wire in
the field. We can now apply this relationship
using the numbers we’ve been given. 𝐵 is equal to 0.2 newtons divided
by four amperes times one meter.
And if we consider just the units
for a moment, a newton per ampere meter, that’s equal to what’s called a tesla,
symbolized capital 𝑇. This is the SI base unit of
magnetic field strength. So 𝐵 is equal to 0.2 divided by
four times one tesla, which is equal to 0.05 teslas. That’s the strength of the magnetic
field that the current-carrying wire is in.
