So not only can a magnetic field

exert some force on a moving charge, we’re now going

to learn that a moving charge or a current can actually

create a magnetic field. So there is some type

of symmetry here. And as we’ll learn later when

we learn our calculus and we do this in a slightly more

rigorous way, we’ll see that magnetic fields and electric

fields are actually two sides of the same coin, of

electromagnetic fields. But anyway, we won’t worry

about that now. And I think it’s enough to

ponder right now that a current can actually induce

a magnetic field. And actually, just

a moving electron creates a magnetic field. And it does it in a surface of a

sphere– I won’t go into all that right now. Because the math gets a little

bit fancy there. But what you might encounter in

your standard high school physics class– that’s not

getting deeply into vector calculus– is that if you

just have a wire– let me draw a wire. That’s my wire. And it’s carrying some current

I, it turns out that this wire will generate a magnetic

field. And the shape of that magnetic

field is going to be co-centric circles

around this wire. Let me see if I can draw that. So here I’ll draw it just like

how I do when I try to do rotations of solids in

the calculus video. So the magnetic field would go

behind and in front and it goes like that. Or another way you can think

about it is if– let’s go down here– is on the left

side of this wire. If you say that the wire’s in

the plane of this video, the magnetic field is popping

out of your screen. And on this side, on the right

side, the magnetic field is popping into the screen. It’s going into the screen. And you could imagine

that, right? You could imagine if, on this

drawing up here, you could say this is where it intersects

the screen. All of this is kind of

behind the screen. And all of this is in

front of the screen. And this is where it’s

popping out. And this is where it’s popping

into the screen. Hopefully that makes a

little bit of sense. And how did I know that it’s

rotating this way? Well, it actually does come out

of the cross product when you do it with a regular

charge and all of that. But we’re not going to go

into that right now. And so there’s a different

right hand rule that you can use. And it’s literally you hold

this wire, or you imagine holding this wire, with your

right hand with your thumb going in the direction

of the current. And if you hold this wire with

your thumb going in the direction of the current, your

fingers are going to go in the direction of the

magnetic field. So let me see if I

can draw that. I will draw it in blue. So if this is my thumb, my thumb

is going along the top of the wire. And then my hand is curling

around the wire. Those are my knuckles. Those are the veins

on my hand. This is my nail. So as you can see, if I was

holding that same wire– let me draw the wire. So if I was holding that same

wire, we see that my thumb is going in the direction

of the current. So this is a slightly new

thing to memorize. And what is the magnetic

field doing? Well, it’s going in the

direction of my fingers. My fingers are popping out

on this side of the wire. They’re coming out on this

side of the wire. And they’re going in, or

at least my hand is going in, on that side. It’s going into the screen. Hopefully that makes sense. Now, how can we quantify? Well, before we quantify, let’s

get a little bit more of the intuition of what’s

happening. It turns out that the closer

you get to the wire, the stronger the magnetic field, and

the further you get out, the weaker the magnetic field. And that kind of makes sense

if you imagine the magnetic field spreading out. I don’t want to go into too

sophisticated analogies. But if you imagine the magnetic

field spreading out, and as it goes further and

further out it kind of gets distributed over a wider and

wider circumference. And actually the formula I’m

going to give you kind of has a taste for that. So the formula for the magnetic

field– and it really is defined with a cross product

and things like that, but for our purposes we won’t

worry about that. You’ll just have to know that

this is the shape if the current is going in

that direction. And, of course, if the current

was going downwards then the magnetic field would just

reverse directions. But it would still

be in co-centric circles around the wire. But anyway, what is the

magnitude of that field? The magnitude of that magnetic

field is equal to mu– which is a Greek letter, which I will

explain in a second– times the current divided

by 2 pi r. So this has a little bit

of a feel for what I was saying before. That the further you go out–

where r is how far you are from the wire– the further you

go out, if r gets bigger, the magnitude of the magnetic

field is going to get weaker. And this 2 pi r, that

looks a lot like the circumference of a circle. So that gives you

a taste for it. I know I haven’t proved

anything rigorously. But it at least gives you a

sense of, look there’s a little formula for circumference of a circle here. And that kind of makes

sense, right? Because the magnetic

field at that point is kind of a circle. The magnitude is equal at an

equal radius around that wire. Now what is this mu, this thing

that looks like a u? Well, that’s the permeability

of the material that the wire’s in. So the magnetic field is

actually going to have a different strength depending on

whether this wire is going through rubber, whether it’s

going through a vacuum, or air, or metal, or water. And for the purposes of your

high school physics class, we assume that it’s going

through air normally. And the value for air

is pretty close to the value for a vacuum. And it’s called the permeability

of a vacuum. And I forget what

that value is. I could look it up. But it actually turns

out that your calculator has that value. So let’s do a problem,

just to put some numbers to the formula. So let’s say I had this current

and it is– I don’t know, the current is equal

to– I’m going to make up a number. 2 amperes. And let’s say that I just pick

a point right here that is– let’s say that that’s

3 meters away from the wire in question. So my question to you is what

is the magnitude in the direction of the magnetic

field right there? Well, the magnitude is easy. We just substitute

in this equation. So the magnitude of the magnetic

field at this point is equal to– and we assume that

the wire’s going through air or a vacuum– the

permeability of free space– that’s just a constant, though

it looks fancy– times the current times 2 amperes

divided by 2 pi r. What’s r? It’s 3 meters. So 2 pi times 3. So it equals the permeability

of free space. So let’s see. The 2 and the 2 cancel

out over 3 pi. So how do we calculate that? Well, we get out our trusty

TI-85 calculator. And I think you’ll be maybe

pleasantly surprised or shocked to realize that– I

deleted everything just so you can see how I get there–

that it actually has the permeability of free

space stored in it. So what you do is you go to

second and you press constant, which is the 4 button. It’s in the built-in

constants. Let’s see, it’s not

one of those. You press more. It’s not one of those,

press more. Oh look at that. Mu not. The permeability

of free space. That’s what I need. And I have to divide

it by 3 pi. Divide it by 3– and

then where is pi? There it is. It’s over the power sign. Divided by 3 pi. It equals 1.3 times 10 to

the negative seventh. It’s going to be teslas. The magnetic field is going to

be equal to 1.3 times 10 to the minus seventh teslas. So it’s a fairly weak

magnetic field. And that’s why you don’t have

metal objects being thrown around by the wires behind

your television set. But anyway, hopefully that gives

you a little bit– and just so you know how it

all fits together. We’re saying that these moving

charges, not only can they be affected by a magnetic field,

not only can a current be affected by a magnetic field

or just a moving charge, it actually creates them. And that kind of creates a

little bit of symmetry in your head, hopefully. Because that was also true

of electric field. A charge, a stationary charge,

is obviously pulled or pushed by a static electric field. And it also creates its own

static electric field. So it’s always in the

back of your mind. Because if you keep studying

physics, you’re going to actually prove to yourself that

electric and magnetic fields are two sides

of the same coin. And it just looks like a

magnetic field when you’re in a different frame of reference,

When something is whizzing past you. While if you were whizzing along

with it, then that thing would look static. And then it might look a

little bit more like an electric field. But anyway, I’ll leave

you there now. And in the next video I will

show you what happens when we have two wires carrying current parallel to each other. And you might guess that they

might actually attract or repel each other. Anyway, I’ll see you

in the next video.

Cool. Had this in physics class a couple months ago, now it makes even more sense.

Sal could you (or maybe someone else who knows) tell me where I can get that TI85 emulator? Is it commercial?

Spectacular explanation

than you.

Does the shape of this magnetic field that disipates based on the radius from the moving electron, form a sphere by adding up growing and shrinking concentric circles?

Does the intensity of the mag field associated with electron x, move along the wire with electron x? So it would be like a spherical field force moving a foot with every foot of distance moved by electron x?

But if electron x causes a mag field, this field is not affecting the electron field in the previous second so it seems like it creates a huge undefinable mess of electron fields that cannot be rigorously defined.

How do we know which way the current is flowing? Does it flow from positive to negative or the other way around?

NONSENSE

@cheese0cake Right hand rule relates to Protons, conv current deals with protons. If you use left hand rule, your dealing with electron flow

@Ardi1589 i think it is

@Ardi1589 yeh i think so

What is this "mu" that looks like a "u'!! you rock sal

can i just say you are really good at art considering your using a tablet which are hard to use XD

Lovely lessons!

Oh, im going to make the hand blue….very professional 😉

Thanks!

TI-85 is so last decade

Hahahaha "These are the veins on my hand" killed me! xD

a little explanation to the formula B=u0 i /2 (pi) r….

using gauss' theorem's equivalent in magnetics..(Ampere's Circuital Law)…

B.dl=u0.i in gauss law we had..E.dS=Q/e0

so in this case..

B.(2(pi)r)=u0.i dl=2(pi)r for a circle(circumference)

we have to find B…

B=u0.i /2(pi)r

dude i have to say, i loved it, i actually knew this stuff but you make it so easy to learn, appreciate the video a lot.

On the website this is embeded on its only in 360p but here its only in 240p it makes no sense. :S

one question

is there a symbol x in circle denotes inwards whiole the . in circle denotes outward curent

@darkshadowz1994 Do you still have it?!?!

this guy should start a new series: How to draw hands

mu=4pi x 10^-7

i love u (NO HOMO)

I love how you WANT to make us understand, it feels like my teachers just want to get their job done, as if its tedious

lol TI-85… TI-84 Plus all the way 😉

I created a Youtube account just so I could like your videos

salman thank you

شكرا سلمان

I have my exam tomorrow and my teacher explained this is the most un-understandable ways!

you saved my life!

thank you!

how are u so good at drawing hands

Damn those are nice hand drawings

I thought you're supposed to use your left hand for wires??

Seal is an artist

hahah

dat hand

"That's why you don't have metal objects being thrown around by the wires behind your television set"

Hilarious! 😀

youtube.com/watch?v=bSge-qDcS4Y is a wonderful addition to this material.

"For your highschool physics class…"

but what about my college physics with vector calc class lol

(Y) great job ever !!!

Thank you for the method!

God Sal is a great drawer

We were taught at school it left-hand rule lol

You sound like Mircrosoft Sam. But you're awesome.

Jasman Gill, left hand rule is different..

good job..

How is he so smart?

cool

Not a native english. Thought I would not keep up with the video, but you actually explain very clear and understanding. Thanks.

is it bad if i watch these for fun…

I have a doubt whenever I try to define the direction of the magnetic field B: in the wire's plane the direction would be k (defining k as a unit vector that comes out of the page). But if I want to know the direction at all points, should I define a unit angular vector in cylindrical coordinates?

So helpful, man. Thank you.

This also works to describe how coherent self-awareness would go about looking at itself and how energy is in flux because it can't be created or destroyed. The universe being one of those concentric circles.

Energy/magnetism = vector self-awareness

So cool thank you so much sir

Does it matter if the current is carried by holes or electrons? The direction of the field would still be the same? I know current direction would be the same, I am just wondering if this theory is valid for both cases.

What is the physical reason why the field spins counterclockwise to the current's direction?

English is not my first language, I find it difficult to talk with people or understand what they say, but you explained it beautifully, and my doubts are cleared now, thank you Khan Academy 🙂

its cooooooool

first rule of right hand, you can also imagine yourself opening a bottle of water for example in a certain direction in goes up..

You emerged clockwise and anti-clockwise directions

i use fx-570MS casio brand calculator, i cant find the MU. Anyone knows?

Great teacher and a greater artist! Had such a hard time understanding this in lecture but you made me understand it within less then 10min. Thank you!

you should quit youtube and be a professional artist . that hand you drew was on point lol

how do you know everything

please i want to know why the magnetic field created around a wire

@Khan Academy – you have the things backwards: the field around a conductor has a direction found by the LEFT HAND RULE; you are using a RIGHT HAND RULE!

Edit: just looked some more and unfortunately there is no consensus on current polarity. I am a mechanical engineer and also have just completed 6 months of electricians apprenticeship schooling in Canada. And here, current flow is the same as electron flow, negative to positive! Very unfortunate as that is certainly a safety issue for people who work in different countries. You appear to be using positive to negative for current flow direction, so then, of course, the video is correct.

IS THE CURRENT D.C?

If the magnetic field direction sketches explained at 1:50 still doesn't make sense, try to imagine a moving dart. If the pointy end is moving towards you, you only see a dot. If it's moving away, you see the cross from its fins. This obviously applies to current or anything else directed"into" or "out of" the board.

I assumed there wouldnt be a video on this because of the black platform and lack of hands..I stand corrected

In headphones, how does the current flow affect the magnetic poles in the voice coil?

thanks a lot

how to demonstrate the expression you wrote of B created by a wire please?

khan is great

that right hand drawing though hahahah nailed it!

We assume mu (U¡=4pi * 10^-7 T m/A

sir can't you dubbed these videos in Hindi language

Hmm if a coil is producing this field, how can I use another coil to pick this magnetic field up? I don't want to receive the electric field but the magnetic

Is r measured from the edge of the wire or the center. I'm assuming center. My applications involves using several laminations of copper

This concept has been in use for many many years. Scrap yards use this exact same set up.

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

watching this because my teacher suck

Who else mugging these up at 1.25x speed (it still sounds just fine ) a few hours before exam?😂🔫

Thank you so much ! U solved my problem in not more than 3 minutes 😇

not nice

This is the only video on youtube which explains why magnetic field is outside/inside of the plane.

the constant is 1.26 x 10^-6 and pi is 3.14

how then are you getting a repeated 1.3333?

I plugged in those numbers and got 1.19 x 10^-7

I thought it was Epsilon 0

haha, yeah, high school physics… not college

is the mu relative permeability or magnetic permeability?

3:05 Soooo cute!!!!

please redo this video with vector calculus in it.

I learned a different formula. B = k*(I/r). Is it the same, or is it different?

The nail of the thumb is on the wrong side and it made me giggle way too much

how come iron filings arent affected by the magnetic field of the wire when i try it out ?

just fyi Uo = 4pi × 10^-7

Ok it's better.

If I understand well the "+" you draw (magnetic field getting in the screen) is actually the "-" (north pole), right?

투자율 아니고 투과율… 번역…

I love Vector Calculus

Finding the total fluid force on the hemispherical tank amounted to computing

a new kind of integral over a surface, or surface integral. As our course develops, we'll see a great need for integrating both functions and vector fields over nice surfaces like the hemispherical tank.

Because of the complexity and importance of surface integrals, we'll have a whole chapter devoted to them. That same chapter also builds from scratch the Divergence Theorem, one of the most important results of our course.

In the next unit, we'll use what we learned apprenticing for Mr. Adams at Tanks For All The Fish to begin to understand the depth of this remarkable theorem.

omg the drawing is so nice

I can't get a hand that good by drawing on paper, and this dude just straight up draws it with a mouse.

What will happen if I place a magnet in this kind of magnetic fields?

I think the wires would repel each other.

V nice 👍