If you got two positive charges,

we know they're gonna repel.

So if I put these next to each other,

this blue charge would repel

the green charge and vice versa,

but how is that working exactly?

I mean there's nothing in between these charges.

How is the blue charge pushing on the green charge

when it's not even touching it?

So this is kind of a weird thing, right?

If I want to push on something in my room,

I need to walk up to that thing

and actually physically touch it,

and then give it a shove.

Yet this blue charge seemingly exerts a force

on the green charge with just empty space in between, right?

There's no strings here.

What is the mechanism?

So physicists were kind of embarrassed

and concerned about this.

So it was like, all right, we can calculate exactly

how much force there would be on each charge

but we don't really know how that is actually working.

It doesn't seem to be making any sense

that a charge can push on another charge

across potentially vast stretches of the universe here.

This could be a huge distance

and yet somehow this charge over here knows,

ah, there's a charge over here pushing on me.

How is that possible?

This isn't new to electrical forces.

This was a problem when Newton came up

with the force of gravity.

When Newton figured out how to calculate

the force of gravity, he showed, okay,

we can calculate how much the earth is gonna pull

on the moon and people were like,

this is great because now we can calculate

and predict the orbits of the planets and comets.

But when people were like, hey, Newton, that's really cool,

but how is the earth pulling on the moon

when there's nothing in between?

Newton was basically like I don't know exactly

why that works but I know the math

lets me predict it exactly.

And so ever since the time of Newton,

this has been kind of in the back of physicists' minds

for hundreds of years now

as we let up to the electric force.

People were kind of like, all right,

how was this force at a distance actually being transmitted?

Is there something in between here

that's actually letting the earth pull on the moon?

So finally when people were dealing

with this electrical phenomenon,

they decided, all right, it's time,

it's time to answer how the two objects

exert forces on each other

across what a potentially vast distances of space.

The person who came up with an explanation

was named Michael Faraday.

So this is Michael Faraday right here.

He did his science in the 1800s generally regarded

as one of the most important physicist/chemist

of all time really.

What Faraday said is this, he said,

guys, here's how it's working.

So this positive charge over here.

So forget about the other positive.

Forget about this green positive for a minute.

Let's just focus on this blue one.

He said, here's what the blue charge is really doing.

He said this blue charge is creating

an electric field all around it

and we'll abbreviate this electric field with a capital E.

Since it's a vector,

we'll put a little vector arrow over the top.

So Faraday said this positive charge creates

an electric field everywhere around it at all times

whether there's other charges nearby or not.

The electric field gets weaker and weaker

the farther out you go.

So near the charge you've got a big electric field

and then the farther away you go,

the weaker the electric field is.

So this is kind of like a spider web surrounding a spider

except the spider is like the charge

and the web is like the electric field.

Now you gotta be careful.

People see this and they think oh,

this is just like electric force, right?

But this is not a force.

These vectors here are not forces.

This is where people get really mixed up.

They look like forces because people are like

we use arrows to draw forces before.

Aren't these just forces?

They're not.

It's a vector so we represent them with arrows

but the electric field is

not the exact same thing as electric force.

So you gotta keep that straight.

They are not the same thing.

They're very related but they are not the same thing.

Electric force is F.

We represent it with F

and maybe a little e for electric force

and since it's a vector

maybe we can draw it with a vector sign.

But the electric force is

not the same thing as electric field E.

How are they related?

Here's how it works.

So even though the electric field is not a force,

it can cause an electric force on other charges.

So as it stands right now,

if all we had was a positive charge,

creating its electric field in the region surrounding it,

there would be no electric force.

You need two charges to have an electrical force.

This charge is not gonna exert a force on itself.

This blue charge and they keep these all straight.

Let's just give this a name.

We'll call this Q one.

This charge Q one creates an electric field

but that electric field, I'll call it E one

because it's created by Q one.

This E one does not exert a force on Q one.

It will exert a force on any other charges

that wander into this region.

So this electric field that gets created by Q one

just sits and waits patiently

just like a spider web waits around the spider

for another charge to wander in.

Then it will exert a force on it.

Let's put another charge in here.

Let's say this positive charge has wandered into this zone

for some reason who knows why.

If it wanders into this region,

there will be an electric force on this charge.

Here's the story that Michael Faraday told us

that made us feel better

about how this force at a distance works.

Michael Faraday said, "Here's what's really happening.

"This positive charge Q one is creating an electric field

"all around it including this point over here

"where Q two is."

So we'll call this charge Q two.

So there was already an electric field at that point

that was being created by Q one.

Now, when this Q two wanders into this region,

the Q two just has to look at its immediate surroundings.

At this point right here it sees this electric field.

It senses it and it knows,

okay, an electric field pointing to the right.

That's gonna cause a force on me to the right.

So it causes an electric force.

The electric field is not an electric force

but it will cause an electric force on a charge

that wanders around into it.

You might wander how is this any better.

Well it keep things local.

So physicists like it when things stay

what we call a local.

By local, we mean, okay, this charge Q two.

In order to figure out what it should do,

all it has to know about is the things

and the space immediately surrounding it.

So it just samples the electric field

that at this point right here,

it says, oh, there's an electric field pointing this way.

I'm gonna feel an electric force into that direction.

In other words, it doesn't have to know.

It doesn't have to say, oh there's this positive charge

on this other side of the galaxy

and that's the thing exerting a force on me.

Nope, it just knows.

Oh, there's an electric field right here.

That's all I need to know to figure out

the electric force on me.

So that's sort of how Faraday got around this question

of how does one object exert a force on another object

when there's nothing in between.

He said there's a mediator basically

that this first charge creates a field everywhere

including at this point

and then that field is creating a force on this charge

that wanders into that zone.

So yes, conceptually the way you could think

about it is this.

This charge Q one is creating the electric field E one.

This electric field in this region is causing a force

on this charge Q two

and that's how Q two knows to feel the force

it's supposed to feel which keeps things local.

This Q two just has to know about the field right

in its vicinity in order to figure out what to do.

It doesn't have to know about things

on the other side of the universe.

But you could complain at this point.

You might be like, "Wait a minute.

"Doesn't Q two also create its own electric field?

"Wouldn't Q two also create an electric field

"every where around it?"

We could call that E two

since it's created by charge too.

Doesn't it create its own electric field

just like all charges do?

Yeah, it does.

In fact it will create an electric field over here

next to Q one and that's how Q one knows

it's supposed to feel the force it feels

in the direction that it feels it.

So that's how these charges talk to each other.

You could think about it that way.

The way charges talk to each other

is with the electric field.

One charge creates an electric field

over by the other charge.

That charge feels the force.

The other charge creates a field by the first charge.

That first charge feels the force.

So conceptually that's how this electric field works

and that's how it does.

So at this point you might not be impressed.

You might be like, "Are we just making up a story

"to make ourselves feel better here?

"Is this just some elaborate fairy tale that makes us

"so that we don't feel so awkward

"talking about things exerting forces

"on each other at a distance?

"Is there any benefit for doing this?"

And there is, there's a big benefit.

Mathematically in terms of physics,

talking about the electric field

makes describing the physics way easier.

In fact it makes it so that you don't even have to know

about the charge creating that field at all.

If you have a way of knowing the field

even if you don't know what charge is creating that fied,

you could figure out what the force is gonna be

on any charge in that field without even knowing

the charge that created that field

and that turns out to happen a lot.

So knowing the electric field is extremely useful.

It lets you determine the electric force on a charge

even if you don't know what charge is exerting that force.

So up to this point, I've been trying to motivate

why we would want this idea of the electric field,