The subject of this
video is Faraday's law.
This one of the astounding and
unexpected results in all of physics.
Let's check, where are we?
We have a law that says the integral of E
dot dr around a closed path is equal to 0.
We defined an electric potential
function V(r2) minus V(r1)
is the negative integral
from r1 to r2 from E dot dr.
If the integral of E dot dr around
the closed path were not equal to 0,
clearly the right hand side
of this equation would
be non-zero while the left
side is automatically zero.
You cannot define the electric potential
function unless the integral of E
dot dr is equal to zero,
a conservative electric field.
We applied this to
circuits with batteries,
capacitors and resisters and everything
worked just the way it was suppose to.
We were probably very proud of ourselves.
But then some experiments
were done that defied our
understanding of integral
of E dot dr equals zero.
This is a permanent magnet.
I can demonstrate that by showing
that it attracts pieces of metal.
We have a loop of wire that
has some resistance r.
If we integrate around the closed path,
the integral of E dot dr is
equal to IR across the coil and
zero because there's no power supply.
Since R is not zero, I is zero, and if we
look on this meter, there is no current.
If I now take this permanent magnet and
let it approach the loop,
a current begins to flow.
When I pull it out of the loop the current
flows in the opposite direction.
Put the magnet in,
it flows for an instant.
Pull it out, it flows for an instant.
If I turn the magnet over when I
bring the magnet into the coil,
it flows opposite to
the way it did before.
Pull it out, again opposite.
According to our law,
there should be no current whatsoever.
But when the magnet is moving,
a current flows.
If I take the same magnet and
I just run it past the coil,
a current flows and again a current flows.
The changing magnetic flux through this
loop is causing a current to flow.
Totally contrary to our
understanding of circuits.
Here we have a device where when I press
this button, it makes a current flow.
I nought cosine omega t,
changing direction 60 times.
So instead of changing the magnetic field
by bringing a permanent magnet closer and
drawing it farther from a loop,
I will let the magnetic field be
changed by the varying current.
Here is a loop of wire.
No power supply.
There is some resistance.
A large resistance in
the filament of the light bulb.
The integral of E dot dr is equal to IR.
There is no power supply if the integral
of E dot dr is equal to zero.
The current must be zero.
What if I bring it near a time
varying magnetic field?
According to our law,
nothing should happen.
But when I do, the light goes on.
Another example,
instead of changing the magnetic field,
suppose we simply change the angle
between our loop and the magnetic field.
Here we have permanent magnets which
cause a horizontal magnetic field.
When I turn this crank, I'm simply turning
a loop through the magnetic field.
So, I'm not changing B and
I'm not changing the area.
I'm changing the angle between
the B field and the area.
[SOUND] This is how all
electric generators work.
Either you turn a loop
through a magnetic field or
you turn magnets through
a stationary loop.
Clearly our law that the integral of E
dot dr is equal to zero is not valid.
We need a law that says
you may induce a current
by having a time varying
magnetic flux through a loop.
Elegantly stated,
the integral of E dot dr is equal to
the negative time derivative
of the integral of B dot ds.
The minus sign.
The convention that you integrate
keeping the area to the palm
side of your right hand, and
your thumb indicates the direction of ds,
are consistent with what
is called Lenz's law.
We will find that whenever
you induce a current
by changing magnetic flux,
the direction of the induced current
must be such as to oppose
the change that makes it.
This is called Lenz's law.
