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MARKUS KLUTE:
Welcome back to 8.20.

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So this section is a preview
or maybe a review of 8.02

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depending on whether or
not you have listened

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to electromagnetism
[? already. ?] So first I just

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want to remind you how we relate
electric and magnetic fields

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and how we can describe
them from a different moving

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reference [? point. ?] So if
the reference point moving in x

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direction, then the x component
of the fields do not change.

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But the transverse
components do change,

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as we have discussed before.

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The core of this
section is about how

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the fields-- the electric
and magnetic fields

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are actually
generated by charges

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and their distributions.

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And this relation is described
by Maxwell's equation.

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The entirety of 8.02 are
classes on electromagnetism

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is about how to understand
Maxwell's equations.

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So I'll do this here in a
very short and brief manner.

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So you can write
Maxwell equations

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in four different equations.

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The first one is
called Gauss's law.

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And if you read the
equation, it just

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says that the divergence
of an electric field

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gives the density of
the source or the charge

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density of the source.

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You can also read this equation
by saying a charge density

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generates an electric field.

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So charges generate
electric fields.

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Similarly, Gauss's
law for magnetism

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can be read as magnetic charges
generate magnetic fields.

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Or the diversion of
the magnetic field

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is the density of
the magnetic source.

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However in nature, we haven't
observed magnetic monopoles

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or at least not yet.

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And so therefore,
there's no such thing.

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There's no magnetic density.

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You can read this equation also
saying that all magnetic field

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lines need to be closed.

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And so that's another
way to look at this.

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And we have Faraday's
law, which means

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that we can induce
electric fields

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in a coil equal to negative
change of the magnetic field.

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In other way, if you want
to create an electric field,

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you can do this with a charge.

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Or you can do this by changing,
as a function of time,

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the magnetic field.

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Changing magnetic fields
generate electric fields.

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And very similarly, we
can look at Ampere's law

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and saying that changing
electric fields generate

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magnetic fields.

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And you can also generate
magnetic fields with a current,

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as we have seen in the
previous [? section. ?]

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So this is how we can
understand [INAUDIBLE] Maxwell's

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equations.

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The difficulty
now, 8.02, is often

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to understand the concept
of fields, the fact

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that there is a
[? vector ?] describing

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the strengths of
this abstract thing,

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of an electric or magnetic
field somewhere in space or

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[INAUDIBLE] are
changing this time.

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That's [? complicated. ?]

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And then there is
also a little bit

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of functional analysis
needed in order to understand

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and how to apply the electric
field by a specific charge.

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Those cases can often
be simplified by having

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symmetric configurations,
like a charged atmosphere,

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or a point charge,
or a cylinder,

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or charges along the line.

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In those cases, those
integrals or those divergences

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can be calculated in a
straightforward manner.

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OK, so then there's
another aspect

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which is relating
[? charge/discharge ?]

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distributions or
fields to forces.

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And that's done
by Lorentz force.

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So the force of the
charged particles

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which is moving in
electromagnetic field

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is given by the strength
of the charge itself

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times the electric field, plus
the velocity of the charge,

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plus the strength of
the magnetic field.

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OK, what that means is I can--

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if I put a charge in an electric
field, it's being pulled.

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It's being accelerated.

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If I have a moving charge
in a magnetic field,

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it's being bend around or
the force bending it around.

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And then I can have this
relativistic equation

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of motion, which uses our
relativistic equation of motion

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and sets it equal to
our Lorentz force.