MARKUS KLUTE: Welcome back to 8.20.
So this section is a preview or maybe a review of 8.02
depending on whether or not you have listened
to electromagnetism [? already. ?] So first I just
want to remind you how we relate electric and magnetic fields
and how we can describe them from a different moving
reference [? point. ?] So if the reference point moving in x
direction, then the x component of the fields do not change.
But the transverse components do change,
as we have discussed before.
The core of this section is about how
the fields-- the electric and magnetic fields
are actually generated by charges
and their distributions.
And this relation is described by Maxwell's equation.
The entirety of 8.02 are classes on electromagnetism
is about how to understand Maxwell's equations.
So I'll do this here in a very short and brief manner.
So you can write Maxwell equations
in four different equations.
The first one is called Gauss's law.
And if you read the equation, it just
says that the divergence of an electric field
gives the density of the source or the charge
density of the source.
You can also read this equation by saying a charge density
generates an electric field.
So charges generate electric fields.
Similarly, Gauss's law for magnetism
can be read as magnetic charges generate magnetic fields.
Or the diversion of the magnetic field
is the density of the magnetic source.
However in nature, we haven't observed magnetic monopoles
or at least not yet.
And so therefore, there's no such thing.
There's no magnetic density.
You can read this equation also saying that all magnetic field
lines need to be closed.
And so that's another way to look at this.
And we have Faraday's law, which means
that we can induce electric fields
in a coil equal to negative change of the magnetic field.
In other way, if you want to create an electric field,
you can do this with a charge.
Or you can do this by changing, as a function of time,
the magnetic field.
Changing magnetic fields generate electric fields.
And very similarly, we can look at Ampere's law
and saying that changing electric fields generate
magnetic fields.
And you can also generate magnetic fields with a current,
as we have seen in the previous [? section. ?]
So this is how we can understand [INAUDIBLE] Maxwell's
equations.
The difficulty now, 8.02, is often
to understand the concept of fields, the fact
that there is a [? vector ?] describing
the strengths of this abstract thing,
of an electric or magnetic field somewhere in space or
[INAUDIBLE] are changing this time.
That's [? complicated. ?]
And then there is also a little bit
of functional analysis needed in order to understand
and how to apply the electric field by a specific charge.
Those cases can often be simplified by having
symmetric configurations, like a charged atmosphere,
or a point charge, or a cylinder,
or charges along the line.
In those cases, those integrals or those divergences
can be calculated in a straightforward manner.
OK, so then there's another aspect
which is relating [? charge/discharge ?]
distributions or fields to forces.
And that's done by Lorentz force.
So the force of the charged particles
which is moving in electromagnetic field
is given by the strength of the charge itself
times the electric field, plus the velocity of the charge,
plus the strength of the magnetic field.
OK, what that means is I can--
if I put a charge in an electric field, it's being pulled.
It's being accelerated.
If I have a moving charge in a magnetic field,
it's being bend around or the force bending it around.
And then I can have this relativistic equation
of motion, which uses our relativistic equation of motion
and sets it equal to our Lorentz force.