funding for this program 
was provided by....

in a game of ice hockey,

scoring three goals in one game 
is called a hat trick.

Ifd like to pull off 
a hat trick today.

I'd like to tell you 
what an electric field is,

solve a problem
infield theory

that Isaac Newton had
a great deal of trouble with,

and introduce 
an important mathematical idea

know as Gauss' Law.

That will
be easier than it sounds

because of the vivid imagination
of a genius

named Michael Faraday.

Faraday's life 
would have embarrassed 

the most shameless novelist.

He began in the most 
modest circumstances.

He had little formal education.

He eventually wound up
being apprenticed

to became a bookbinder.

He was intent 
on self-improvement

and started attending 
public scientific lectures

at the royal institution
in London.

He was so enthralled
by those lectures

that he begged for the chance

to do the most menial work
at the royal institution.

He eventually wound up

as the professor of the royal institution

and the most famous scientist 
in Europe.

Throughout his career,

Faraday understood mathematics
so poorly

that he couldnft read 
the scientific papers

of his own competitors.

Yet he had an intuition
that got him to the core

of every scientific problem.

Itfs one of the greatest ideas 
that we want to discuss.

Itfs the idea of lines
of constant electric force

radiating everywhere
throughout apace.

In the field of Physics,

surely no tool has dug up
more scientific truth

than the sharp spade
of Mathematics.

Yet when he uncovered
the field theory,

the groundwork from which 
much of modern physics grows,

Mathematics was a tool 

that Michael Faraday
had to work without,

but he was exposed to one idea

that was essentially 
Mathematical in nature.

In 1789,

Charles Augustin Couloumb
confirmed

what the scientific community
had suspected for years.

Couloumb finally demonstrated

that the electric force is
inversely proportional

to the square of the distance
between the charges.

As elegant
as Couloumbfs experiment was,

the concept,

the idea
of the inverse square relation,

had been
a major scientific notion

for some time.

A century earlier, in fact,

Isaac Newtonfs theory stated
that the fall of an apple

and the orbit of the moon

were both consequences

of the same basic laws.

One of those laws,

the law
of universal gravitation,

states that any two masses
attract each other

with a force 
inversely proportional

to the square
of the distance between them.

This was a difficult law
to apply,

even for Isaac Newton himself.

To make the point, 
Hefd have to show

that when an objectfs
attracted to the Earth,

in acts as if
all of the Earthfs mass

were concentrated at the center.

And more difficult,
Hefd have to rationalize

What he called
gaction at a distance.h

A phrase making 

That such bodies
As the Earth and the Sun

Apply forces
Directly to each other

even though theyfre separated 
my millions of kilometers

with no tangible connection
between them.

Though the great genius 
Was often testy,

Even he himself 
Might have come to admit

a certain dissatisfaction

with the idea
of action at a distance.

Perhaps somewhat defensively
In the principia, Newton wrote,

gI have not been able
to discover

the cause of those properties
of gravity,

and I feign no hypothesis.h

Newton felt
no obligation to explain

by either physical
or Michel means

the law of gravity.

gTo us it is enough

that gravity does really exist.h
He added,

gAnd act according to the laws
which we have explained.h

Obviously, that was enough.

In England thereafter,

the law of gravitation was
the law of the land.

By the 19th century,

with the law of gravitation 
firmly established,
 
Newtonfs followers
had discovered

that electricity and magnetism 
obey similar laws.

In all of them,

the force decreases

with the square of the distance.

The similarity is amazing.

The question is, why?

Perhaps because
the inverse-square law

is related to 
a simple geometrical property

of three-dimensional spaces

and perhaps because these forces

arenft the only things 
that diminish
with the square of distance.

The essence
of the inverse-square law

can be seen 
in the concept of flux,

the Latin word meaning flow.

Light flows out from the Sun
equally in all directions.

But imagine a sphere
enclosing the Sun.

All the light would 
pass through the sphere,

no matter what its distance 
from the Sun.

And the area of a sphere grows
As the square of its radius.

So the amount of light energy
per unit area decreases

as the square of distance.

The inverse-square law wasnft 
the only provocative idea

to which Faraday was exposed
as a young man.

By 1819,

he was a regular visitor 
at the royal institution,

particularly at the lectures

of the institutionfs 
legendary professor

Sir Humphrey Davy,

chemist and natural philosopher,
a scholar who was knighted,

made a Baronet, 

and president 
of the royal society,

Davy was the very crest
of British science.

With his own research
As the subject,

Davy spoke
as the worldfs authority

on every element
from Sodium to Potassium, 

Chlorine to Iodine.

Davy became
a scientific father figure
for Faraday

and remained a mentor 
and enormous influence

for almost 20 years,

although the relationship was,
At time, a rocky one.

Under Davyfs influence,
in the golden age of chemistry,

none shone brighter 
than Michel Faraday.

He discovered Benzene,
liquefied chlorine gas,

and developed
new alloys of steel.

The list of his remarkable
accomplishments as a chemist

goes on and on.

Nonetheless, in 1821,

Faraday set aside
his work in chemistry.

In that year, Oersted discovered

the effect electric current
has on magnets.

While that effect
can be seen clearly now,

in 1821, it was still 
a great scientific mystery.

Indeed, why would 
the compass needle

line up perpendicular
to the electric current?

Sparked by curiosity
to begin with

and asked by an editor
to write an article

that would end 
the scientific confusion,

Faraday set out

to solve the mystery
for himself.

Faraday saw the force
of an electrical current

and invented a device to do it.

That device happened to be
the first electric motor.

How did Michel Faraday
manage that?

Perhaps because, being unable
to analyze them mathematically,

Faraday was able to take 
these circular magnetic forces

at face value.

In any case,
to Michel Faraday,

electricity,
as well as magnetism,

applied real forces in space.

He began his study of them
with a number of assumptions.

Anywhere in the vicinity
of an electric charge,

a small test charge 
experiences a force.

If itfs due to only one charge,

the patternfs of forces
detected by the test charge

is simple.

The patternfs more complex
For two opposite chargesc..
or for two charges
of the same signc.

And more complex still

for more complicated
arrangements.

But in any case,
herefs the point.
 
Even if the test charge
isnft there to feel it,

the pattern of forces can be 
imagined to exist

everywhere in space.

This although Faraday 
only imagined it,

the field can also be
expressed mathematically.

The force that acts
on a test charge

an each point in space

is equal to the test charge

times a quantity
due only to the other charges.

That quantity is 
the electric field.

Faraday never arrived

at that definition
of the electric field,

but by seeing both
electric and magnetic phenomena

as forces in space,

he managed 
to see further than his peers.

As a result of this 
and many other discoveries,

he eventually became director 
of the research laboratory

at the royal institution,

and, succeeding Davy,
he became the professor there,

as well as a member
of the royal society.

It was as researcher
rather than instructor

that he saw deeper and deeper

into the invisible forces
of space.
To Faraday,
the 1/R squared force

between electric charges

suggested that the force
must be applied

Uchida Mitsuko

by something
radiating outward from changes,

something which,
like light from the sun,

never stops and never ends
in space.

as faraday imagined it,

this something world be
lines or tubes,

each an capable
of apprying a force

to any change in its path.

these lines of force world begin
only on positive charges

and end only on negative ones.

and theyworld flow
smoothly through space,

never crossing or tangling.

no matter the configuration,

the charges world have

a characterristic
pattern of lines.

the force they apply
world be strong

near the charges where the lines
are crowded together

and weak far from the changes,

where the lines are
farther apart.

the ability to apply a force
recides at each point in space.

the force arises
from the intensity of lines

regardless of the location
of the charges that create them.

even without
such space-age graphics,

this is how faraday pictured
the electric field.

it still seems
the most graphic way

to visualize one.

satisfyring
the sientific community

would take
another step or two.

necessarily, those steps
would be mathematical.

one of the more important
was taken

by karl friedrich gauss.

physicist...

astronomer...

and perhaps
the best mathematician

of all time.

gauss' mathematics would offer
an elegant conplement

to faraday's idea,

and it would become law.

in faraday's terms,

flux is represented
by all the lines of force

passing through any surface.

gauss's law states
that for any closed surface,

the total flux is proportional

to the net electric dharge 
inside a surface,

any posititve flux out word
through it

must be balanced

by an equal amount 
of inward, or negative, flux.

gauss' law,

which gives 
mathematical definition

to faraday's intuitive notion

about the electric field,

is actually an expression

of the geometric meaning

of any inverse-squared law.

in appropriate form,

it applies not only

to electric fields,

but to gravitational

and magnetic fields as well,

and even to light 
flowing from the sun.

in any event,

gauss' theoretical work

combined 
with farada's common sense

reveals a number
of amazing facts

about nature itself.

for example, watch what happens 
inside a conductor

where a lattice of positive ions 
is neutralized

by mobile 
and constantly moving electrons.

an electric field
passing through a conductor

forces the electrons to flow

until they pile up
at the surface,


repelling the motion
of further electrons.


but that means
the electric field


inside any conductor

becomes equal to zero

when electorostatic equilibrium
is estabrished.

therefore,a closed surface
inside the conductor

has no flux through it.

so the net charge inside
must be zero

but there can be charge
at the surface,

and no matter what's outside,

the surface charge
makes the field inside

equal to zero.

and since
all the action's at the surface,

a metal box of any sort,

even a flimsy,
screen-covered cage,

can keep out an electric field.

that fact can be demonstrated
with this device,

a gold-leaf electroscope.

notice how it responds

to the field
of an electric charge.

notice, too, that even when

an electroscope's
inside the cage,

it reacts
in the same fashion.

however,
when the box is enclosed,

an electric field can't enter
to disturb the gold leaf.

any metal box can do it.

and to this  day,

any metal box that does do it

is called a faraday cage.

not every faraday cage

was desingned
to project its contents

from electric fields.

[radio playing]

the steel girders of a bridge
or the scaffolding of a tunnel

probaboly couldn't care less

about keeping electric fields
at bay,

but they do
a pretty effective job of it.

why? because radio waves

are a kind of disturbance
in the electric field

and because,
whether it's a bridge

or the enclosed container
that its name implies,

a faraday cage
isn't a great place

to get good reception.

[music fades]

[music playing]

outside again,
the reception's fine.

in any case, while cars bcan go
just about anywhere,

where can the lines

of a uniform
sphere of charge go?

an extended region of charge

might consist
of many point charges in space.

but if it's symmetrical,

the electric field has only
one place togo,

and that's outward.

according to gauss' law,

the flux through
a closed surface outside

depends only
on the totalcharge.

if the charged region
is a sphere,

the size makes no difference.
so, in other words,

the electric field outside
is the same,

whether the charge is
uniformly disturbted

in a sphere

or concentrated at a point
at the center.

by the same reasoning,

because it depends only
on its inverse-square nature,

the gravitational force
of the earth is the same

as if all its mass
were concentrated at the center.

isaac newton had to use
his most powerful mathematics

to prove that point,

which may have contributed
to the 20-year delay

in the publication
of the principia,

but with the help

of michael faraday's
vivid mental picture,

the reason behind the idea
can be perceived

and completely grasped

without any mathematics
whatsoever.

not that mathematics
wouldn't apply.

after all, in the end,

the best scientific expression
of faraday's ideas,

indeed, the ultimate triumph

of the electromagnetic field
theory

would be
the mathematical expression

of james clerk maxwell.

faraday wold come
to admire maxwell,

and, quite properly,

the admiration
would go both ways.

responding to a letter
from faraday, maxwell wrote,

"you are the first person

"in whom the idea of bodies
acting at a distance

"has arisen as a principle
to be actually believed in.

"nothing is clearer
than your descriptions.

"you seen to see
the lines of force

"curving round obstacles
and driving plumb at conductors

"and swerving towards
certain directions

"in crystals

"and carrying with them
everywhere

"the same amount
of attractive power

spread wider or denser
as the lines widen or contract."

thinking of gravity
as well as electricity,

maxwell concluded,

"your lines of force
can weave a web across the sky

and lead the stars
in their courses."

so faraday had this idea

about lines of force
filling all of space.

there's no doubt
that faraday believed

that those lines
were really there.

then along came
james clerk maxwell.

he transmuted faraday's idea

into our modern view 
of the electric field.

once that was done,

faraday's lines of force
no longer existed.

a reasonable question
you might ask is,

why do we bother teaching you

something we no longer beleve
to be true?

you might get some perspective
of the atom

is made up of smaller particles
called protons and neutrons.

we can smash the nucleus apart

and get out
the protons and neutrons

and study them,
so we know they're real.

we also believe today

that protons and neutrons
are made up

of even smaller
inner constituents

which are called quarks,

but it's impossible
to smash a proton apart

and get out
the individualquarks.

the quarks are forever hidden

inside of the protons
and neutronds.

the question that arises
in view of that--

are quarks real?

that question is very similiar
to the question

of whether faraday's
lines of force are real.

in the long run,

it may turn out
to be irrelevant.

faraday's lines of force
were a mental scaffolding

that had to be put up

in order to build
the final edifice

which was the electric field.

once the building is finished,

the scaffolding
can be torn down,

but that makes it
no less important

because the building
couldn't have been constructed

without the scaffolding.

someday, it may torn out
that even the idea of quarks,

which today's scientists
certainly believe are real,

turned out to be

just a kind
of mental scaffolding.

we'll get onn with studying

the final edifice
of electric theory

when we meet next time.

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captioning performed by
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captions copylight 1986
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the mechanical universe
is a college corse

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end of file