Coulomb's law | Physics | Khan Academy

- [Instructor] We encounter
so many different kinds

of forces in our day-to-day lives.

There's gravity, there's
the tension force,

friction, air resistance,

spring force, buoyant forces,

and so on and so forth, but guess what?

Not all these forces are fundamental.

Gravity is certainly
one of the fundamental

forces of nature,

but turns out that most other forces

that we encounter in our daily life

are actually a manifestation
of the electromagnetic forces.

These are the forces
responsible for all the electric

and magnetic phenomena and
most of the other forces

that we encounter in everyday life,

but how do electromagnetic
forces give rise

to all of these?

Well, let's get a glimpse
of that in this video.

Now, there are two parts to these forces,

the electric part and the magnetic part.

We will save the magnetic
part for future videos.

In this video, we'll just
stick to electric part of it,

and even there, we'll talk
about a particular kind

of electric force,

which you call the electrostatic forces.

Electrostatic,

which we also call static electricity.

from the word itself, you can see electro

means we're taking to electric part,

and static means stationary,

where things are not moving a lot,

or maybe they're moving very slowly.

The reason to do that is because
we wanna take baby steps.

So first, we'll consider what happens

when we have static conditions,

then we'll see what happens
when they're moving,

and so on and so forth, okay?

All right.

So, when it comes to gravity,

we'll keep comparing with gravity,

'cause we are familiar with gravity, okay?

When it comes to gravity,

where does the force of gravity come from?

What is it due to?

Well, we know that the
force of gravity comes

from a fundamental property
of matter, which we call mass.

Things that have mass will produce

gravitational force on each other, right?

Similarly, what causes
electrostatic force?

Well, turns out electronic force comes

from a property of matter called,

you've probably heard of this, charge.

Anything that has charge will put forces

on other things that have charge.

Now, an immediate question
that we could have

is, hey, if that is the case,
and if matter has charge,

and because of the charge,

they put electrostatic
forces on each other,

why don't we notice that?

Why don't we notice electrostatic
forces between, say,

planets and stars, and
all of those things?

Why don't we notice that in everyday life?

Well, first of all, we do
notice them in everyday life,

and which we will see in
this particular video,

but the reason why we don't
notice them on a large scale

is, well, it's a good question,
and we'll come back to that.

But anyways, if you want
to see electrostatic

forces in action,

it's better to start looking at things

inside the atom, so, let's do that.

We've probably seen the model of an atom.

We have the nucleus at the center,

which contains protons and neutrons,

and we all have, you know,
kind of like an electron cloud

that surrounds a nucleus,

where you have electrons over there.

Now, these particles will have charge.

Protons have a positive charge,

neutrons are neutral, they have no charge,

and electrons have a negative charge.

Okay, but we may be wondering,

how much charge do protons
and electrons have?

To answer that question, we need to know

the unit of the charge.

Just like how mass has
a unit of kilograms,

charge has a unit of
something called the Coulomb,

named after the scientist,
Charles Coulomb,

who did a lot of work on this,

and same way we use is capital C.

Now, it turns out that
protons and electrons

have the same magnitude of the charge.

They have different signs, but
they have the same magnitude,

and we call that that number, e,

and that happens to be roughly 1.602

times 10 to the power -19 Coulombs,

so, it's a very tiny value
in terms of Coulombs.

And so, we would now say
that the charge on the proton

is this much positive,

so, we'll just call it +1e.

The charge on the electron
is this much negative,

so, -1e,

and the charge on the
neutron, well, that is zero.

It has no charge, so,
its charge is just zero.

And now, we can immediately
see a big difference

between mass and charge.

Mass, there's only one kind,

but charge, there are two
kinds, positives and negatives,

and this will now help
us understand something.

An atom has the same number
of protons and electrons,

so, the total charge of the
atoms would just be zero,

because the charge of the proton

and charge of the electron
will just cancel out,

and so, the atom itself will be neutral.

And so, if you consider big objects,

which has billions and billions of atoms,

it's pretty much neutral,

because the total number of
protons is pretty much the same

as total number of electrons,

and that's the reason
why most things around us

are uncharged,

or they might have a few
extra electrons or protons,

so will have a very tiny
charge, but mostly uncharged,

and that's why we don't
see electrostatic forces

in action most of the time.

That's why at celestial scales,

we don't see electrostatic
forces in action,

because they're mostly uncharged,

or they have very tiny charge,

but at the microscopic
level, we do see it.

We see protons putting
forces on other protons,

and other electrons of the
same atom, of a different atom.

They're all there,

but if you want to study these forces,

the next big question we should ask

is what is the strength of this force?

How much force would,
say, a proton would put

on, say, another proton, or
maybe on another electron?

How do we figure that out?

Well, for that, let's assume
that we have two, in general,

let's consider two charged particles.

Let's call these charges as q1 and q2.

You can imagine, for example,
these are two pieces of paper,

and, you know, these pieces of paper

have some extra electrons, or
some extra protons, let's say.

So, they are charged,

so, they will put an
electrostatic force on each other.

The question we wanna try to answer

is what is the direction of that force,

and what is the strength of that force?

What does that depend on?

Let's start with the
direction of the force.

Positives will push and
repel other positives.

Negatives will push and
repel other negatives.

In other words, like charges
will repel on each other,

but unlike charges will
attract each other.

A proton will attract an electron.

Positives will attract negatives.

So, the direction of the force
depends upon their charge,

the polarity of that charge.

If both are positive or both
are negative, they will repel.

If one is positive, the
other one is negative,

they will attract.

For simplicity, let's just assume one.

Let's just just say
that both are positive,

then they would repel each other.

So, this is a repulsive
electrostatic force.

Another big question is
what does the strength

of this force depend on?

Why don't you pause the video,

and just think about how you
think they would be related

to q1 and q2, the charges,
and the distance between them?

Okay, since the electrostatic
forces come from the charges,

we would expect that these
forces must be directly related

to q1 and q2.

If either of them increase,
we would expect the force

to increase.

And how would it be
related to the distance?

Well, if you put them farther away,

well, we expect the
force to become smaller.

If you put them very far
away, we would expect them

to not interact with
each other at all, right?

On the other hand, if
we bring them closer,

that means if you make this smaller,

the distance to be smaller,

you would expect the force to be larger.

Closer they are, larger the force,

which means you would expect
an inwards relationship

with the distance between them.

Now, if you put it all together,

we'll get something
called the Coulomb's Law,

and that looks like this.

Notice the Coulomb's Law
is giving us something

very similar to what we predicted.

It is, directly, the force
between the two charges

is directly related to
the charges themselves,

you can see that,

and it is inversely related
to the distance between them.

And more importantly,
you can see an inverse

square relationship.

Where have we seen an inverse
square relationship before?

Hey, we've seen it in gravity.

We've seen the force of gravity,

the universal law of
gravitation is very similar.

Over here, G, which we call
the universal constant,

its value was about this much.

So, what is the value of K,

which we call the Coulomb's constant?

Well, it turns out that the value

of the Coulomb's constant, K, is about,

is about 8.99 times 10
to the power 9 units.

And can you work out the units yourself?

Well, we just have to
isolate K on one side,

and if you do that, let
me do that very quickly,

we'll get F times R squared
divided by q1 and q2,

so, that will be F is newtons,

R squared is meter squared,

divided by q1 and q2 is Coulombs squared.

Yeah, I don't have to remember them.

I never remember them,

because I can always rearrange

and then figure out what the units are,

but that's the value of K.

And now that you know this,

if you know the value of the charges,

and you know how far they are,

we can plug in and figure
out the force between them.

Okay, so, let's quickly compare these two.

Well, the one similarity
is the inverse square law.

The farther you put
them, the farther you go,

the smaller the force gets, the
force dies out very quickly,

but what about some differences?

Well, the first difference
is you can see gravity

is always attractive,

but the electrostatic force
can be attractive or repulsive.

That's because we have two kinds

of charges over here, right?

But there's another thing that we can see.

Look at the value of K.

It's much bigger compared
to the value of G

in standard units.

From this, we can kind of
guess that the Coulomb's Law

is much, much stronger
than the force of gravity,

which means, if you take,
for example, two protons,

and compare the force of gravity

with the electrostatic
force, the Coulomb's force,

you'll find the Coulomb's
force to be way stronger,

orders of magnitude stronger
than the force of gravity.

And so, that's why at
this microscopic scale,

we can completely ignore
the force of gravity.

It's the electronic force that dominates,

but as we saw, once we
go at a much more larger

celestial scale,

well, now, the masses are so huge,

and the charges are so
small that the force

of gravity dominates.

I absolutely love this, how the, you know,

at different scale, the
different forces dominates,

and now, we are in a
position to understand that.

That's incredible, isn't it?

But that's not all.

Now, we are in a position to
answer our original question,

how electromagnetic forces
or electrostatic forces

get manifested as some of
the daily forces that we see?

For example, tension, where
does tension come from?

Well, if you had to zoom into a string,

you'll see a lot of, you
know, atoms over there.

And although atoms are neutral,

since because they have
positives and negatives inside,

they can push and pull on other, you know,

electrons and protons.

For example, the protons can
push on the other protons,

the protons can pull on the electrons,

the electrons over here can
push on the other electrons,

the electrons over here
can pull on the protons,

so, there are a lot of forces out there,

and, you know, we can model
and say that, you know,

pretty much all these forces balance out.

They have to, because,
look, a string is, you know,

pretty much static,

so, you can assume that most of the atoms

are pretty much static,
so, they are all balanced,

and therefore, the net
force on all of the atoms

are pretty much zero.

We say they're in equilibrium.

Now, what happens when
you pull on the string?

Let's say, you put a mass on, you know,

attach a mass over here,

and because of gravity,
it pulls on the string.

Well, now, because of that pull,

some of the atoms will
start moving farther away

from each other.

Equilibrium gets disturbed.

Net force is no longer zero.

It turns out for the string,

because the equilibrium gets disturbed,

and the atoms go away from each other,

the net force will try
to bring them closer

back to each other,

and that is how tension force
is generated in a string.

Isn't that wonderful?

It all comes from the
electrostatic forces.

Similarly, think about
where does the force

of friction come from?

Well, again, if we were
to zoom in over here,

we will see that, you know,

although things look
smooth at a macroscale,

on a microscopic scale,
things are not really smooth,

and if we zoom in even further, again,

we will notice that the atoms of the box

can interact with the atoms of the floor

via other electrostatic forces,

and it's these electrostatic
forces which all add up

and puts, you know, and it all adds up,

and gives rise to the force of friction.

Again, it is super complicated.

We'll not try to understand
exactly how the force

of friction comes, why it opposes, say,

the force of, you know,

why it opposes motion, for
example, in some cases,

but it all comes from
the electrostatic forces.

And we can use the same
idea, the same model

to explain spring forces, air resistances,

buoyant forces, pretty
much contact forces,

other contact forces
that you pretty much see

in your daily life,

and I find it absolutely fascinating

that even though these
models are not very accurate,

I mean, today, we have
better, more accurate models,

what we call quantum mechanical models

to explain all these phenomena better,

but even if we ignore that,
even if we consider, you know,

simpler models, like
we are doing over here,

we can just use the idea
of electrostatic forces,

the Coulomb's forces to
try and get an intuition

behind how it manifests as
most of these daily forces

that we encounter in life.

I find that absolutely beautiful.