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- [Instructor] So here's a question.

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If you got two positive charges,

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we know they're gonna repel.

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So if I put these next to each other,

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this blue charge would repel

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the green charge and vice versa,

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but how is that working exactly?

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I mean there's nothing
in between these charges.

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How is the blue charge
pushing on the green charge

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when it's not even touching it?

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So this is kind of a weird thing, right?

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If I want to push on something in my room,

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I need to walk up to that thing

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and actually physically touch it,

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and then give it a shove.

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Yet this blue charge
seemingly exerts a force

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

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There's no strings here.

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What is the mechanism?

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So physicists were kind of embarrassed

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and concerned about this.

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

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how much force there
would be on each charge

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

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It doesn't seem to be making any sense

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that a charge can push on another charge

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across potentially vast
stretches of the universe here.

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This could be a huge distance

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and yet somehow this
charge over here knows,

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

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How is that possible?

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This isn't new to electrical forces.

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This was a problem when Newton came up

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with the force of gravity.

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When Newton figured out how to calculate

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the force of gravity, he showed, okay,

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we can calculate how much
the earth is gonna pull

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on the moon and people were like,

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this is great because now we can calculate

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and predict the orbits of
the planets and comets.

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

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but how is the earth pulling on the moon

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when there's nothing in between?

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Newton was basically
like I don't know exactly

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why that works but I know the math

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lets me predict it exactly.

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And so ever since the time of Newton,

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

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for hundreds of years now

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as we let up to the electric force.

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People were kind of like, all right,

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how was this force at a distance
actually being transmitted?

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Is there something in between here

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

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So finally when people were dealing

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with this electrical phenomenon,

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they decided, all right, it's time,

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it's time to answer how the two objects

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exert forces on each other

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across what a potentially
vast distances of space.

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The person who came up with an explanation

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was named Michael Faraday.

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So this is Michael Faraday right here.

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He did his science in the
1800s generally regarded

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as one of the most
important physicist/chemist

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of all time really.

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What Faraday said is this, he said,

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guys, here's how it's working.

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So this positive charge over here.

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So forget about the other positive.

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Forget about this green
positive for a minute.

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Let's just focus on this blue one.

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

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He said this blue charge is creating

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an electric field all around it

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

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Since it's a vector,

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

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So Faraday said this
positive charge creates

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an electric field everywhere
around it at all times

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whether there's other
charges nearby or not.

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The electric field gets weaker and weaker

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the farther out you go.

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

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and then the farther away you go,

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the weaker the electric field is.

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

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except the spider is like the charge

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and the web is like the electric field.

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Now you gotta be careful.

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People see this and they think oh,

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this is just like electric force, right?

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But this is not a force.

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These vectors here are not forces.

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This is where people get really mixed up.

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They look like forces
because people are like

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we use arrows to draw forces before.

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Aren't these just forces?

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They're not.

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It's a vector so we
represent them with arrows

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but the electric field is

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not the exact same
thing as electric force.

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So you gotta keep that straight.

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They are not the same thing.

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

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Electric force is F.

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We represent it with F

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and maybe a little e for electric force

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and since it's a vector

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maybe we can draw it with a vector sign.

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But the electric force is

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not the same thing as electric field E.

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How are they related?

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Here's how it works.

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So even though the electric
field is not a force,

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it can cause an electric
force on other charges.

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So as it stands right now,

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if all we had was a positive charge,

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creating its electric field
in the region surrounding it,

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there would be no electric force.

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You need two charges to
have an electrical force.

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This charge is not gonna
exert a force on itself.

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This blue charge and they
keep these all straight.

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Let's just give this a name.

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We'll call this Q one.

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This charge Q one
creates an electric field

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

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because it's created by Q one.

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

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It will exert a force on any other charges

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that wander into this region.

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So this electric field
that gets created by Q one

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just sits and waits patiently

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just like a spider web
waits around the spider

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for another charge to wander in.

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Then it will exert a force on it.

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Let's put another charge in here.

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

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for some reason who knows why.

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If it wanders into this region,

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there will be an electric
force on this charge.

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Here's the story that
Michael Faraday told us

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that made us feel better

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about how this force at a distance works.

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

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"This positive charge Q one
is creating an electric field

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"all around it including
this point over here

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"where Q two is."

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So we'll call this charge Q two.

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So there was already an
electric field at that point

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that was being created by Q one.

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Now, when this Q two
wanders into this region,

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

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At this point right here it
sees this electric field.

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It senses it and it knows,

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okay, an electric field
pointing to the right.

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

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So it causes an electric force.

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The electric field is
not an electric force

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but it will cause an
electric force on a charge

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that wanders around into it.

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You might wander how is this any better.

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Well it keep things local.

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So physicists like it when things stay

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what we call a local.

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

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In order to figure out what it should do,

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all it has to know about is the things

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and the space immediately surrounding it.

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So it just samples the electric field

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that at this point right here,

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

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

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

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

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on this other side of the galaxy

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

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Nope, it just knows.

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Oh, there's an electric field right here.

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That's all I need to know to figure out

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the electric force on me.

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

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of how does one object exert
a force on another object

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when there's nothing in between.

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He said there's a mediator basically

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that this first charge
creates a field everywhere

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including at this point

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and then that field is
creating a force on this charge

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that wanders into that zone.

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So yes, conceptually
the way you could think

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about it is this.

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

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This electric field in this
region is causing a force

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on this charge Q two

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

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it's supposed to feel
which keeps things local.

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This Q two just has to
know about the field right

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

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It doesn't have to know about things

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on the other side of the universe.

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But you could complain at this point.

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You might be like, "Wait a minute.

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

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"Wouldn't Q two also
create an electric field

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"every where around it?"

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We could call that E two

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since it's created by charge too.

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Doesn't it create its own electric field

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just like all charges do?

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Yeah, it does.

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In fact it will create an
electric field over year

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

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it's supposed to feel the force it feels

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in the direction that it feels it.

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

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You could think about it that way.

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The way charges talk to each other

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is with the electric field.

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One charge creates an electric field

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over by the other charge.

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That charge feels the force.

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The other charge creates a
field by the first charge.

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That first charge feels the force.

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So conceptually that's how
this electric field works

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and that's how it does.

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So at this point you
might not be impressed.

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

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"to make ourselves feel better here?

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"Is this just some elaborate
fairy tale that makes us

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"so that we don't feel so awkward

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"talking about things exerting forces

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"on each other at a distance?

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"Is there any benefit for doing this?"

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And there is, there's a big benefit.

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Mathematically in terms of physics,

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talking about the electric field

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makes describing the physics way easier.

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

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about the charge creating
that field at all.

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If you have a way of knowing the field

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

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you could figure out what
the force is gonna be

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on any charge in that
field without even knowing

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the charge that created that field

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and that turns out to happen a lot.

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So knowing the electric
field is extremely useful.

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It lets you determine the
electric force on a charge

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

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

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why we would want this
idea of the electric field,

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why physicists would
come up with this idea.

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But I wouldn't blame you if at this point

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you aren't thinking, I still don't know

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what electric field is.

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I know what it isn't.

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Electric field is not electric force

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but what exactly is the electric field.

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So let me give the electric
field a proper definition here.

259
00:09:06,652 --> 00:09:08,875
The electric field E at a point in space

260
00:09:08,875 --> 00:09:12,241
is defined to be the
amount of electric force

261
00:09:12,241 --> 00:09:15,481
per charge exerted at that point in space.

262
00:09:15,481 --> 00:09:17,281
So this is what the electric field is.

263
00:09:17,281 --> 00:09:19,892
It's the force per charge.

264
00:09:19,892 --> 00:09:22,255
The way physicists usually
think about this is

265
00:09:22,255 --> 00:09:24,254
imagine throwing a test charge in here.

266
00:09:24,254 --> 00:09:25,756
We call this a test charge.

267
00:09:25,756 --> 00:09:28,041
We'd like to imagine that
this charge is really little

268
00:09:28,041 --> 00:09:30,921
so that it doesn't completely
likes swamped and overwhelmed.

269
00:09:30,921 --> 00:09:32,883
The other charge is creating this field.

270
00:09:32,883 --> 00:09:35,439
Otherwise if you threw
some huge charge in here,

271
00:09:35,439 --> 00:09:37,147
all the other charge would scatter

272
00:09:37,147 --> 00:09:38,831
and it would change the whole situation.

273
00:09:38,831 --> 00:09:42,213
So let's say we put a really
small test charge in here.

274
00:09:42,213 --> 00:09:44,484
If I want to know what the
electric field is at a point

275
00:09:44,484 --> 00:09:47,028
in space, I'd just bring
my test charge over here,

276
00:09:47,028 --> 00:09:50,626
measure the amount of electric
force on that test charge

277
00:09:50,626 --> 00:09:53,480
and then I just divide
by how much was there

278
00:09:53,480 --> 00:09:54,560
in that test charge.

279
00:09:54,560 --> 00:09:56,436
What was the charge of that test charge?

280
00:09:56,436 --> 00:09:57,853
I'll call this charge two.

281
00:09:57,853 --> 00:09:59,994
If I take the force on charge two,

282
00:09:59,994 --> 00:10:01,749
divide it by charge two,

283
00:10:01,749 --> 00:10:03,971
that would be the value
of the electric field

284
00:10:03,971 --> 00:10:05,429
at that point in space.

285
00:10:05,429 --> 00:10:07,562
So this is how we define
the electric field.

286
00:10:07,562 --> 00:10:09,092
The definition of electric field is

287
00:10:09,092 --> 00:10:11,045
the amount of force per charge.

288
00:10:11,045 --> 00:10:12,492
In other words, let's
put some numbers in here.

289
00:10:12,492 --> 00:10:14,740
Let's say Q two was two coulombs.

290
00:10:14,740 --> 00:10:17,153
This is actually an
enormous amount of charge.

291
00:10:17,153 --> 00:10:19,284
This is kind of unrealistic example

292
00:10:19,284 --> 00:10:21,131
but it will make the numbers come out nice

293
00:10:21,131 --> 00:10:22,534
and conceptually it's the same thing.

294
00:10:22,534 --> 00:10:25,295
So a positive two
coulombs was placed here.

295
00:10:25,295 --> 00:10:26,812
That's the value of Q two.

296
00:10:26,812 --> 00:10:29,367
Let's say when we measure
the force on Q two,

297
00:10:29,367 --> 00:10:31,680
we're getting 10 newtons of force.

298
00:10:31,680 --> 00:10:32,958
In that case, we can just say,

299
00:10:32,958 --> 00:10:34,461
"All right, then the electric field,

300
00:10:34,461 --> 00:10:36,287
"in that region of that vicinity

301
00:10:36,287 --> 00:10:40,445
"is gonna be 10 newtons of
force per two coulombs of charge

302
00:10:40,445 --> 00:10:43,099
"and we get an electric field of five.

303
00:10:43,099 --> 00:10:45,492
"Then the units are newtons per coulomb."

304
00:10:45,492 --> 00:10:47,310
And that makes sense because
what the electric field

305
00:10:47,310 --> 00:10:50,506
is really telling you is
how many newtons of force

306
00:10:50,506 --> 00:10:52,646
you would get per coulomb.

307
00:10:52,646 --> 00:10:54,988
If you put more coulombs
at that point in space,

308
00:10:54,988 --> 00:10:56,767
there'd be a greater force.

309
00:10:56,767 --> 00:10:59,089
This number is telling
you the number of newtons

310
00:10:59,089 --> 00:11:00,898
you would get per coulomb.

311
00:11:00,898 --> 00:11:03,544
Since we had two coulombs
at this point in space

312
00:11:03,544 --> 00:11:06,081
and there was five newtons per coulomb,

313
00:11:06,081 --> 00:11:07,555
the force was 10 newtons.

314
00:11:07,555 --> 00:11:10,437
So this number five newtons
per coulomb is important

315
00:11:10,437 --> 00:11:12,882
because it's the same for
any charge you put there.

316
00:11:12,882 --> 00:11:14,718
This is why the electric field is useful.

317
00:11:14,718 --> 00:11:16,706
At this point in space right here,

318
00:11:16,706 --> 00:11:18,661
if the electric field is five,

319
00:11:18,661 --> 00:11:20,192
it's five newtons per coulomb

320
00:11:20,192 --> 00:11:21,809
no matter what charge you put there.

321
00:11:21,809 --> 00:11:24,167
So if I put a four coulombs
charge at that point,

322
00:11:24,167 --> 00:11:27,092
since there's five
newtons for every coulomb,

323
00:11:27,092 --> 00:11:28,946
there'd be a 20 newton force there

324
00:11:28,946 --> 00:11:31,346
because there's five
newtons for every coulomb.

325
00:11:31,346 --> 00:11:35,298
If there's four coulombs, there'd
be five times four newtons

326
00:11:35,298 --> 00:11:36,638
which is 20 newtons.

327
00:11:36,638 --> 00:11:39,059
So you can imagine rearranging
this formula another way.

328
00:11:39,059 --> 00:11:41,148
You could just multiply those sides by Q

329
00:11:41,148 --> 00:11:43,900
and you get that the
electric force on a charge

330
00:11:43,900 --> 00:11:47,967
is equal to the value of that
charge at that point in space

331
00:11:47,967 --> 00:11:50,713
multiplied by the value
of the electric field

332
00:11:50,713 --> 00:11:52,052
at that point in space.

333
00:11:52,052 --> 00:11:54,428
But it's important to note
this electric field is

334
00:11:54,428 --> 00:11:57,005
not created by this charge Q two.

335
00:11:57,005 --> 00:11:59,161
This was created by some other charge

336
00:11:59,161 --> 00:12:00,791
or collection of charges.

337
00:12:00,791 --> 00:12:05,308
Remember this charge Q one is
creating this electric field

338
00:12:05,308 --> 00:12:08,132
E one and that electric field is causing

339
00:12:08,132 --> 00:12:10,248
this electric force on Q two.

340
00:12:10,248 --> 00:12:14,226
Q two did not create
the electric field E one

341
00:12:14,226 --> 00:12:15,564
that it interacted with.

342
00:12:15,564 --> 00:12:19,122
Q one created that electric field E one.

343
00:12:19,122 --> 00:12:20,117
So people get mixed up.

344
00:12:20,117 --> 00:12:21,234
They see this formula.

345
00:12:21,234 --> 00:12:22,067
They start to think

346
00:12:22,067 --> 00:12:25,414
maybe this Q two is creating
this electric field.

347
00:12:25,414 --> 00:12:26,377
It's not.

348
00:12:26,377 --> 00:12:29,084
This electric field is
causing the electric force

349
00:12:29,084 --> 00:12:31,451
on that charge, not the other way around.

350
00:12:31,451 --> 00:12:33,782
This Q two is not creating this field.

351
00:12:33,782 --> 00:12:37,148
This field is causing
the force on that charge.

352
00:12:37,148 --> 00:12:39,450
So this formula is extremely useful.

353
00:12:39,450 --> 00:12:42,267
If you know the electric
field at a point in space,

354
00:12:42,267 --> 00:12:44,958
you can figure out the
electric force on any charge

355
00:12:44,958 --> 00:12:48,162
at that point by just multiplying
the two values together

356
00:12:48,162 --> 00:12:49,762
to get the electric force.

357
00:12:49,762 --> 00:12:51,607
So you can see now that the electric field

358
00:12:51,607 --> 00:12:53,560
is not the electric force.

359
00:12:53,560 --> 00:12:56,351
It's the amount of
electric force per charge

360
00:12:56,351 --> 00:12:57,574
at a point in space.

361
00:12:57,574 --> 00:12:59,878
Very related but different.

362
00:12:59,878 --> 00:13:02,593
Different enough that you have
to keep these ideas separate.

363
00:13:02,593 --> 00:13:06,346
Electric field is not electric
force, and vice versa.

364
00:13:06,346 --> 00:13:08,297
Electric force is not electric field.

365
00:13:08,297 --> 00:13:09,745
The electric field is the amount

366
00:13:09,745 --> 00:13:11,456
of electric force per charge

367
00:13:11,456 --> 00:13:14,380
and the electric force on a
charge at some point in space

368
00:13:14,380 --> 00:13:17,097
is the amount of charge
times the electric field

369
00:13:17,097 --> 00:13:18,430
at that point in space.

370
00:13:18,430 --> 00:13:21,721
So recapping, electric charges
create electric fields.

371
00:13:21,721 --> 00:13:24,539
These electric fields
enter and cause forces

372
00:13:24,539 --> 00:13:27,420
on charges that exists in that region.

373
00:13:27,420 --> 00:13:29,641
The value of the electric
field is representing

374
00:13:29,641 --> 00:13:32,393
the number of newtons of force per coulomb

375
00:13:32,393 --> 00:13:33,639
at that point in space.

376
00:13:33,639 --> 00:13:35,498
In terms of a formula, the electric field

377
00:13:35,498 --> 00:13:37,668
is the amount of force per charge

378
00:13:37,668 --> 00:13:39,755
or in other words the
amount of electric force

379
00:13:39,755 --> 00:13:42,759
is the charge times the electric field

380
00:13:42,759 --> 00:00:00,000
at that point in space.