- [Voiceover] I have an interesting set up over here.
I have a magnetic field that is constant,
and it's going straight out of the surface of this loop.
The magnitude of the magnetic field
at any point of the surface is going to be 'B'.
What's interesting here is this loop that we have,
This right part of the loop is movable.
You can imagine it's a cylinder
that can roll to the right,
and the magnitude of it's velocity,
we're going to say is lowercase 'v'.
And this cylinder, lets say it has length 'L'
Given that, you can see that we're going
to have a change in magnetic flux.
Why are we gonna have a change in magnetic flux,
or a change in magnetic flux through the surface?
Well if this thing is moving to the right,
when it's speed is 'v'
it can be any units, meters per second,
or whatever it is.
Even though the magnetic field itself is
constant, you're actually going to be changing the area,
the area that is, I guess you could, contained by
this loop, and so that is going to
give us a change in flux
And if you have a change in flux that is
going to induce an electromotive force,
or it's going to induce a voltage in this loop
which will cause a current to flow.
Let's think about what that electromotive force
that's going to be induced is going to be.
I'm just gonna rewrite Faraday's law right over here.
Faradays law: negative 'N' times
our change in flux, and we're talking
about our change in flux over change in,
let me write that a little bit neater,
our change in flux over change in time.
The 'N' is the number of loops we're talking about.
So in this case, 'N' is just going to be one
and the negative, I've already complained
a little bit about in previous videos.
This is really just reminding us
the math, when you're not using proper vector mathematics,
this just reminds us that this 'Emf'
is going to cause a current to go through this loop,
and the magnetic field that is
induced by that current will go against the direction
of our change in flux. That's just something to remind us.
What we really care about is
our change in flux over change in time.
What is that going to be?
Let me just write it here,
our change in flux over change in time.
Our change in flux in this case
is going to be our change in
our, the magnitude of our magnetic field
that is going perpendicular to the surface
times the area of our surface
over our change in time.
What is this going to be equal to?
'B' is constant, it's not going to change
over the time that we care about.
So the change in 'B' times 'A'
is really going to be 'B' times our change in area.
'B' times our change in area over how much time goes by.
So what is our change in area going to be?
Let's say we let delta 't' , let's say delta 't' happens,
what is going to be our change in area?
Let's let delta 't' go on.
If delta 't' goes on, this cylinder,
or if we wait for 't' units of time,
or if 't' units of time go by,
let me do this in another color,
I'm gonna use this color right over here.
How far will we go after delta 't'?
We know the magnitude of our velocity
if you multiply the magnitude of your velocity
times your change in time,
that will give you your distance.
Your change in area is going to be
the amount of distance it's travelled
times the length of the rod, which is just that.
Our change in area, which is that area right over there,
our change in area over that time
is going to be the distance this rod goes.
Notice this rod is going in a direction
that is perpendicular to the direction of the magnetic field
that's an important thing to realize.
We have our change in area is going to be
this dimension which is how far the rod travels
times the length of the rod, that's how much area we gain,
that's how much our area increases,
times the length of the rod, that's our change in area.
We can substitute that back over here.
This is going to be equal to,
we got our 'B', we have our change in time,
and our change in area we just said is going to be,
Let me just write it this way,
I could write is as the length of our rod
times the magnitude of our velocity, or our speed
times our change in time.
Well, change in time divided by change in time,
those cancel out. Our change in flux over that time
or our average rate of change in flux
we see simplifies to the length of our rod
times the magnitude of our velocity,
or our speed, times the magnitude of the magnetic field
that is going perpendicular to the surface.
This is something that you will see many times
in your physics class, this whole notion of
if your rod going in a perpendicular direction
to a magnetic field, it induces
an electromotive force of 'LvB'
This is where it's coming from,
it's coming directly from Faraday's law.
You can say, okay, if that's happening,
what direction is the current going to actually flow in?
If the magnetic field isn't changing,
but since the area is increasing,
the flux is increasing in the upward direction.
You can say the flux is increasing in that direction.
The current that gets induced,
and the magnitude of the current is going to be,
based on how much resistance we have,
but the current is going to induce a magnetic field
that goes against our change in flux.
Let's see, if the current went that way, what will happen?
I'm going to take my right hand out,
put my thumb in that direction,
and if I were to loop my fingers around,
this would, if we went that way, this would describe,
this would induce a magnetic field
that goes like this.
That actually would enhance
the flux going through the, or change in flux,
going the same direction of the change in flux,
We've already talked about this,
would violate the law of conservation of energy.
The current's gonna go in the other direction.
It's gonna go, in this case is going to go clockwise,
because the current is going to induce a magnetic field.
Once again, I could take my right hand out,
and try to draw my right hand,
and we can see now, the direction
my fingers go in are that way.
Notice we're looking at the inside of the surface,
the surface area was increasing the flux
in the upward direction, getting more
of the magnetic field in the upward direction,
being contained in the area.
The magnetic field induced by the current that is induced,
or that current that's being caused
by the electromotive force and the magnitude of
the force is going to be dependent on our resistance,
that's going to go in the other direction,
it's going to go down that way.
Or it's going to induce a magnetic field
that is gonna go downwards.
So the current needs to be going clockwise.