Electricity and magnetism
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Electrostatics (part 1): Introduction to Charge and Coulomb's Law
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Electrostatics (part 2)
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Proof (Advanced): Field from infinite plate (part 1)
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Proof (Advanced): Field from infinite plate (part 2)
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Electric Potential Energy
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Electric Potential Energy (part 2-- involves calculus)
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Voltage
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Capacitance
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Circuits (part 1)
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Circuits (part 2)
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Circuits (part 3)
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Circuits (part 4)
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Cross product 1
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Cross Product 2
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Cross Product and Torque
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Introduction to Magnetism
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Magnetism 2
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Magnetism 3
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Magnetism 4
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Magnetism 5
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Magnetism 6: Magnetic field due to current
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Magnetism 7
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Magnetism 8
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Magnetism 9: Electric Motors
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Magnetism 10: Electric Motors
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Magnetism 11: Electric Motors
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Magnetism 12: Induced Current in a Wire
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The dot product
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Dot vs. Cross Product
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Calculating dot and cross products with unit vector notation
Magnetism 6: Magnetic field due to current See how a wire carrying a current creates a magnetic field.
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- 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 nought.
- 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.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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