Let’s imagine that instead of

having two charges, we just have one charge by itself,

sitting in a vacuum, sitting in space. So that’s this charge here, and

let’s say its charge is Q. That’s some number,

whatever it is. That’s it’s charge. And I want to know, if I were to

place another charge close to this Q, within its sphere of

influence, what’s going to happen to that other charge? What’s going to be the

net impact on it? And we know if this has some

charge, if we put another charge here, if this is 1

coulomb and we put another charge here that’s 1 coulomb,

that they’re both positive, they’re going to repel each

other, so there will be some force that pushes the

next charge away. If it’s a negative charge and I

put it here, it’ll be even a stronger force that pulls it

in because it’ll be closer. So in general, there’s this

notion of what we can call an electric field around

this charge. And what’s an electric field? We can debate whether it really

exists, but what it allows us to do is imagine that

somehow this charge is affecting the space around it

in some way that whenever I put– it’s creating a field that

whenever I put another charge in that field, I can

predict how the field will affect that charge. So let’s put it in a little more

quantitative term so I stop confusing you. So Coulomb’s Law told us that

the force between two charges is going to be equal to

Coulomb’s constant times– and in this case, the first

charge is big Q. And let’s say that the second

notional charge that I eventually put in this field

is small q, and then you divide by the distance

between them. Sometimes it’s called r because

you can kind of view the distance as the

radial distance between the two charges. So sometimes it says r squared,

but it’s the distance between them. So what we want to do if we want

to calculate the field, we want to figure out how much

force is there placed per charge at any point around this

Q, so, say, at a given distance out here. At this distance, we want to

know, for a given Q, what is the force going to be? So what we can do is we could

take this equation up here and divide both sides by this small

1, and say, OK, the force– and I will arbitrarily

switch colors. The force per charge at this

point– let’s call that d1– is equal to Coulomb’s constant

times the charge of the particle that’s creating the

field divided by– well, in this case, it’s d1–

d1 squared, right? Or we could say, in general–

and this is the definition of the electric field, right? Well, this is the electric field

at the point d1, and if we wanted a more general

definition of the electric field, we’ll just make this a

general variable, so instead of having a particular distance,

we’ll define the field for all distances

away from the point Q. So the electric field could be

defined as Coulomb’s constant times the charge creating the

field divided by the distance squared, the distance we are

away from the charge. So essentially, we’ve defined–

if you give me a force and a point around this

charge anywhere, I can now tell you the exact force. For example, if I told you that

I have a minus 1 coulomb charge and the distance is equal

to– oh, I don’t know. The distance is equal to let’s

say– let’s make it easy. Let’s say 2 meters. So first of all, we can say,

in general, what is the electric field 2 meters

away from? So what is the electric

field out here? This is 2, right? And it’s going to be

2 meters away. It’s radial so it’s actually

along this whole circle. What is the electric

field there? Well, the electric field at

that point is going to be equal to what? And it’s also a vector

quantity, right? Because we’re dividing a vector

quantity by a scalar quantity charge. So the electric field at that

point is going to be k times whatever charge it is divided

by 2 meters, so divided by 2 meters squared, so that’s 4,

right, distance squared. And so if I know the electric

field at any given point and then I say, well, what happens

if I put a negative 1 coulomb charge there, all I have to do

is say, well, the force is going to be equal to the charge

that I place there times the electric field

at that point, right? So in this case, we said the

electric field at this point is equal to– and the units for

electric field are newtons per coulomb, and that

makes sense, right? Because it’s force divided

by charge, so newtons per coulomb. So if we know that the electric

charge– well, let me put some real numbers here. Let’s say that this

is– I don’t know. It’s going to be a really large

number, but let’s say this– let me pick

a smaller number. Let’s say this is 1

times 10 to the minus 6 coulombs, right? If that’s 1 times 10 to the

minus 6 coulombs, what is the electric field at that point? Let me switch colors again. What’s the electric field

at that point? Well, the electric field at

that point is going to be equal to Coulomb’s constant,

which is 9 times 10 to the ninth– times the charge

generating the field– times 1 times 10 to the minus

6 coulombs. And then we are 2 meters

away, so 2 squared. So that equals 9 times 10 to

the third divided by 4. So I don’t know, what is that? 2.5 times 10 to the third or

2,500 newtons per coulomb. So we know that this is

generating a field that when we’re 2 meters away, at a radius

of 2 meters, so roughly that circle around it, this is

generating a field that if I were to put– let’s say I were

to place a 1 coulomb charge here, the force exerted on that

1 coulomb charge is going to be equal to 1 coulomb times

the electric fields, times 2,500 newtons per coulomb. So the coulombs cancel out, and

you’ll have 2,500 newtons, which is a lot, and that’s

because 1 coulomb is a very, very large charge. And then a question you should

ask yourself: If this is 1 times 10 to the negative 6

coulombs and this is 1 coulomb, in which direction

will the force be? Well, they’re both positive,

so the force is going to be outwards, right? So let’s take this notion and

see if we can somehow draw an electric field around a

particle, just to get an intuition of what happens when

we later put a charge anywhere near the particle. So there’s a couple of ways to

visualize an electric field. One way to visualize it is if I

have a– let’s say I have a point charge here Q. What would be the path of a

positive charge if I placed it someplace on this Q? Well, if I put a positive charge

here and this Q is positive, that positive charge

is just going to accelerate outward, right? It’s just going to go straight

out, but it’s going to accelerate at an ever-slowing

rate, right? Because here, when you’re really

close, the outward force is very strong, and then

as you get further and further away, the electrostatic force

from this charge becomes weaker and weaker, or you could

say the field becomes weaker and weaker. But that’s the path of a–

it’ll just be radially outward– of a positive

test charge. And then if I put it here, well,

it would be radially outward that way. It wouldn’t curve the

way I drew it. It would be a straight line. I should actually use

the line tool. If I did it here, it would be

like that, but then I can’t draw the arrows. If I was here, it would

out like that. I think you get the picture. At any point, a positive test

charge would just go straight out away from our charge Q. And to some degree, one measure

of– and these are called electric field lines. And one measure of how strong

the field is, is if you actually took a unit area

and you saw how dense the field lines are. So here, they’re relatively

sparse, while if I did that same area up here– I know

it’s not that obvious. I’m getting more

field lines in. But actually, that’s not a good

way to view it because I’m covering so much area. Let me undo both of them. You can imagine if I had a lot

more lines, if I did this area, for example, in that area,

I’m capturing two of these field lines. Well, if I did that exact same

area out here, I’m only capturing one of the field

lines, although you could have a bunch more in between here. And that makes sense, right? Because as you get closer and

closer to the source of the electric field, the charge

gets stronger. Another way that you could have

done this, and this would have actually more clearly shown

the magnitude of the field at any point, is you could

have– you could say, OK, if that’s my charge Q, you

could say, well, really close, the field is strong. So at this point, the vector,

the newtons per coulomb, is that strong, that strong, that

strong, that strong. We’re just taking

sample points. You can’t possibly draw them

at every single point. So at that point, that’s

the vector. That’s the electric

field vector. But then if we go a little bit

further out, the vector is going to be– it falls off. This one should be shorter, then

this one should be even shorter, right? You could pick any point and you

could actually calculate the electric field vector, and

the further you go out, the shorter and shorter the electric

field vectors get. And so, in general, there’s all

sorts of things you can draw the electric fields for. Let’s say that this is a

positive charge and that this is a negative charge. Let me switch colors so I don’t

have to erase things. If I have to draw the path of

a positive test charge, it would go out radially from

this charge, right? But then as it goes out, it’ll

start being attracted to this one the closer it gets to the

negative, and then it’ll curve in to the negative charge and

these arrows go like this. And if I went from here, the

positive one will be repelled really strong, really strong,

it’ll accelerate fast and it’s rate of acceleration will slow

down, but then as it gets closer to the negative one,

it’ll speed up again, and then that would be its path. Similarly, if there was a

positive test charge here, its path would be like

that, right? If it was here, its path

would be like that. If it was here, it’s path

would be like that. If it was there, maybe its path

is like that, and at some point, its path might never get

to that– this out here might just go straight

out that way. That one would just go straight

out, and here, the field lines would just

come in, right? A positive test charge would

just be naturally attracted to that negative charge. So that’s, in general, what

electric field lines show, and we could use our little area

method and see that over here, if we picked a given area, the

electric field is much weaker than if we picked that

same area right here. We’re getting more field lines

in than we do right there. So that hopefully gives you

a little sense for what an electric field is. It’s really just a way of

visualizing what the impact would be on a test charge

if you bring it close to another charge. And hopefully, you

know a little bit about Coulomb’s constant. And let’s just do a very

simple– I’m getting this out of the AP Physics book, but they

say– let’s do a little simple problem: Calculate the

static electric force between a 6 times 10 to the negative

sixth coulomb charge. So 6 times– oh, no, that’s

not on an electric field. Oh, here it says: What is the

force acting on an electron placed in an external electric

field where the electric field is– they’re saying it is 100

newtons per coulomb at that point, wherever the

electron is. So the force on that, the force

in general, is just going to be the charge times the

electric field, and they say it’s an electron,

so what’s the charge of an electron? Well, we know it’s negative, and

then in the first video, we learned that its charge is

1.6 times 10 to the negative nineteenth coulombs times

100 newtons per coulomb. The coulombs cancel out. And this is 10 squared, right? This is 10 to the positive 2, so

it’ll be 10 to the minus 19 times 10 to the positive 2. The force will be minus

1.6 times 10 to the minus 17 newtons. So the problems are

pretty simple. I think the more important thing

with electric fields is to really understand intuitively

what’s going on, and kind of how it’s stronger

near the point charges, and how it gets weaker as it goes

away, and what the field lines depict, and how they can be used

to at least approximate the strength of the field. I will see you in

the next video.

neutron doesn't have a charge so it's not affected by the field. i think lol.

I like how he doesn't forget anything that would confuse us

its not 2500N its 2250N

Dude there's an vacant teaching position in the physics department at my school, I need you…

When is next part coming???

At 6 mins the electric field is 2250 N/C rather than 2500.

Great video btw

I just commented in the last video about the ambiguity between using d and r! Thanks for clearing that up. Your awesome.

@ 6:30, shouldn't it be 2250 N/C??

I hope in the future only good teachers like you teach, that way student will be able to learn more efficiently.

When I become a millionaire, you are definitely getting a big donation.

I'm pretty sure you could take over the world with your knowledge if you wanted to.

Yup, it should

yes.

I think that's one of the main reasons he's so popular. Even youtube automatic captions gets it right most of the time!! Now that's an achievement!!

(9*10^3)/4=2250

why force between 2 charges is a vector quantity ????????

what happens with the direction…????

plzzz plzz explain ?????

Because Force it's self is a vector quantity, for example Newtons second Law states that F=m * a. In relation to electrostatics it is stating that F= q * E with q being charge and E being the field. Well when the ATTRACTION OR REPULSION of each charge has a magnitude and a DIRECTION, thus being a vector quantity, because if it just had magnitude it would only be a scalar quantity. Hope that helped.

it will have no effect since they are neutrons and thus are neutrally charged

Well, I must say you are having my attention somehow… Superb ! Thumbs Up !

In the exercise why is -q? The charges must attract each other?

right? 😉

CORRECTION…at 6:15; the E should be 2250 N/C; (9*10^3)/4 = 2250 not 2500

Probability says no god

yeah i so agree bro

"Skwaylar" lol

Funny when he keep saying "I don't know" and then put a number

the right answer is 2250 N/C, great lesson, thanks.

aww you got me confused when you said 2500 n but great explanation!!!

It is odd that we have all the mathematics, but we have no objective understanding of what charge is!

what will be the pattern of electric field lines if we consider a dipole..

why are these videos all in 240p?

these are literally saving my grade right now….

At 10:30 Why when a positive and negative charged object kept close for Interaction the direction of the lines go from positive to negative?

I don't know if anyone's pointed it out yet (and it's not a big deal because the concept is spot-on) but around six minutes in, Sal says the E-field is 2500, but it should be 2250.

I vote that "squaler" is made into a new word.

I really appreciate the content but man, did you record that with a hairdryer? Pixels. Pixels everywhere.

9÷4=2.25

SQUALER!!!!!!!!!!!

i learn more on the comments section… but i thank the vid still… if it weren't for the tree there would be no fruit.

psa: GET TO THE FUCKING POINT

This might save my physics grade. Get back to you after tomorrow's exam.

Anybody here for Penovich tomorrow?

pls make better quality vids though atleast 480p…

can someone explain why the fields are curved? I've watched it a few times and didn't catch that if he mentioned it

I'm supposed to be learning this, and im too busy rewinding and laughing at "SQUALER"

I have seen a definition of field strength = F/Q, but why is that? why not F/(2Q)? or F/Q2?, is this word "strength" related to stress-strength as in mechanics?

I have saved all your videos…if I have any doubts I look upon khan academy , it really makes us learn better …but this video m not satisfied, u confusd me. hope u make other video of this with better explanation…..

came to the comments to see if anyone else laughed when he said "squaler" lmaoooo

Coulomb's Law involves vectors. Need vector arrow on the F in the equation. :p

I have seen all the vedios …and I want to see some more vedios to make my concept clear……

so our sun is basically Q, our planets are "baby q", and then that applies to the rest of our planetary systems (obvi atoms as well) and, to follow- our galaxy / Universe. Including black holes which were once the equal to our sun. Which will eventually self destruct and become a black hole … which then creates a new galaxy when the gravity and magnetism attract and form new planets from the destructive aftermath…. the "dust" yes? based on the gravity from the new black hole -creating a new center of gravity?….and this applies to all atoms and any center of "gravity" that creates rotation. but its all basic magnetism. right? curios. sun creates a GIANT charge. attracts our planets (which have minor charge)… its a mirror of the workings of an atom. yes? … … email me if im right or wrong. idk.

just lookin for answers, not mathematics. its obvi not an accident that atoms reflect the solar patterns in our galaxy/ even our Universe. I'm sure the same properties apply in some way shape or form. Enter- magnetic influence. but question – can we relate this entire magnetic influence to dark matter?

The mouse wriggling everywhere across the screen makes it seem like sal is having a seizure during the whole video XD

studying for the mcat 🙁

s q u a l e r

Sqwaler

The balls came instead of the tail , heavy electrons..pfff

Em, just want to say that 9×10^3÷4=2250. It is very helpful, though

I lost it when he said squaler

So helpful, much more helpful than barron's book or anything of that sort.

squaler?seriously??

a squailer quantity

My new PHYSICS SOLVING APP.More then 150+ formulas,Solves for any variable you want,Covers up all physics.download now.https://play.google.com/store/apps/details?id=com.physics.lenovo.myapplication

I still can't get it how is he able to write those equations with mouse only 👏👏👏👏👏

Wish I though of watching these videos before the test and not after. 🙁

I really cant understand this…too difficult!

Khan Sir, first day when I watch your videos I was surprised that how one can write in this way …..digitally…and today I am using it perfectly..this is because of you …Thankful to you for this reason…

at 3:32 where does the -1C go?

Always good videos but this one was kinda haphazard

classic sal

A big Thankyou Sir. keep up teaching us.

ah this finally makes sense now, thanks!

I’m sorry but this just confused me more

what is this, hd for ants?

"I should actually use a line tool…", "…but then i can't draw the arrows…" LOL so cute.

2008 quality be like

What if the charge rotates

There are so many different equations for electric fields ahh

I don't know why I laughed so hard when he said "squalar" lol

I am curious about something. At 9:17 in the explanation of field lines around Q, you say, "as you get closer to the source of the electric field the charge gets stronger" I did not know the charge gets stronger or weaker. I thought a charge was a charge, multiples of either negative or positive increments and was fixed. How does the charge get stronger? Does it accumulate more electrons?

Awful

horrible quality, needs to be re-recorded.

I'm very thankful for these videos, they are very interesting and easy to follow. However, I was wondering why the quality (in terms of resolution and drawings) is so low in some videos.

Content is awesome as always just not happy that i cannot go beyond 240p.

As soon as I heard him say squaler, I scrolled down to see the comments hoping someone commented about it, and low and behold, a comment had been made! Another win for the YT community.

kkkkkk i dont know….thnks it really helped

"the charge times the electric field is great in you" – Yoda, Master

his voice <3

great video

thank you thank you thank you!!!

5:58 That should be 2250 Newtons

So electric field can never be negative? How does is show direction then?

I thought it was E=kQ/r… because if E=Work/Charge, and Work is equal to Force Times distance… then if you derive it in this way, you shoud get E=kQ/r instead of E=kQ/r^2

i like the video but there was really nothing discussed about voltage in this vid

Sir khub valo laglo

I LOVE YOU

Honestly why take a physics class after this chanell

So my father lives in Germany and sometimes I have to leve school for a month to go to Germany because I want to get a sidesens ship and it messes up my grads and when I come back I have a lot of thing to learn a lot of tests to Wright ect and this helps so much I learn sooo much and dont have to cram physics because when I come back I'm usually in front of the class and what thai learn because of you thank you so much u got a new subscriber