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
Electrostatics (part 1): Introduction to Charge and Coulomb's Law Introduction to Charge and Coulomb's Law (video from May 2008 that I forgot to upload)
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- Let's talk a little bit about what I find to be one of the
- more mysterious forces of the universe.
- Actually, I find all of the forces of the universe to be
- fairly mysterious, so let's talk a
- little bit about charge.
- And we've all heard of charge.
- Charge the battery.
- This particle has charge.
- But when you really think about it, all charge means is
- that there's this property called charge, and we know
- that if something contains a positive charge-- and calling
- it positive is a little bit arbitrary.
- It's not like protons have a little plus written on them.
- We could have called them negative.
- But when something has a positive charge and when
- something else has a positive charge, that
- they repel each other.
- We also know that if I had something else, another
- particle that happened to have a negative charge, and once
- again, the word "negative" being applied to this is
- completely arbitrary.
- They could have called it blue charge and red charge, but all
- we know is that when another object has the other charge--
- in this case, we call it negative-- that's going to be
- attracted to a positive charge.
- So what do we know about charge?
- Charge is a property that particles have, and if you put
- enough particles together, I guess objects have that
- property as well.
- So it's just a property.
- And that's a way of saying that I really don't
- know what it is.
- And frankly, no one fundamentally
- knows what it is.
- Actually, no one really fundamentally knows anything.
- But charge is a property of particles and
- objects, just like mass.
- I mean, if you think about it, mass is just a property.
- And to some degree, it seems a little bit more real than
- charge, because our brains are wired to in some way
- comprehend what mass is, but we're probably comprehending
- weight and volume more than mass, but we can think more
- about that at another time.
- Charge is a little bit more abstract because, before we
- started rubbing amber into our hair, we really didn't
- experience much charge unless we got struck by lightning.
- So charge is a property that particles or objects have, and
- we know that there are two types of charge, which we've
- arbitrarily named positive and negative.
- And we know that like charges repel and opposite charges
- attract, or unlike charges attract, right?
- So what can we do with this?
- Well, if we have this property, I think a useful
- thing to do would be to measure the property, and so
- we came up with units, and so the unit of charge is called
- the coulomb.
- It's named after a scientist in the late 1700s, who played
- around a lot with charge.
- You could look up more about him on Wikipedia.
- But it's called the coulomb, and the coulomb-- there's a
- bunch of definitions, but I like to think of it in terms
- of elementary particles, just because, to some degree,
- unless you go into quantum theory and start talking about
- quarks and stuff, the elementary charge is the
- charge on a proton or a neutron.
- So I'll go into more detail in the future on actually the
- structure of atoms and whatever else, but let me just
- draw a little example.
- So an atom tends to have some neutrons in them, which don't
- have this charge property.
- It'll have some protons in them, which
- have a positive charge.
- Once again, that's kind of
- arbitrarily defined as positive.
- We could have called a red charge.
- And then it has these things floating around that are much,
- much, much lighter than the protons and the neutrons in
- the nucleus, and these are called electrons.
- It's not even clear that they're real objects.
- They're almost like energy, but sometimes it's useful to
- view them as objects.
- Sometimes it's useful to view them as--
- well, not as objects.
- And we'll go into all of that more later, but electrons have
- a negative charge.
- And the fundamental unit of charge, as far as we are
- concerned right now before we start talking about quarks and
- other potentially subatomic particles, is the charge in an
- electron or proton.
- And they have the exact same charge, and that elementary
- charge is denoted by e.
- And to be frank, I'm not sure whether e stands for
- elementary or e stands for electron.
- But actually, e is equal to the charge of a proton so it
- probably stands for elementary charge of a proton.
- And the charge of an electron is the negative of this, so
- negative e is the charge of an electron.
- But if we didn't care about sign, then the
- magnitudes are the same.
- So that's the fundamental as far as we know or so far in
- our physics.
- That's the fundamental charge.
- The fundamental unit of charge is just the charge in a proton
- or neutron.
- So how does a coulomb relate to that?
- Well, a coulomb, which we'll denote by C, is equal to-- and
- this is a bit of an arbitrary number, but when we start
- doing things with electricity, we'll see why the coulomb was
- defined the way it is, but a coulomb is 6.24 times 10 to
- the eighteenth e's.
- Or you can say it's 6.24 times 10 to the eighteenth times the
- charge on an electron-- actually, times the charge on
- a proton, and then, of course, in terms of magnitude.
- Because if I just say coulomb, I'm not
- really giving a direction.
- So if you look at it the other way around, you can say that
- the elementary charge is equal to-- at least its magnitude--
- 1.6 times 10 to the minus 19 coulombs.
- So fair enough.
- This might be a useful number to memorize, but it will
- usually be provided for you in some way.
- So what can we do?
- We say that these objects have this property called charge.
- Like charges repel.
- Unlike charges attract.
- If we have enough of these protons together, then the
- whole object has charge.
- If we have more protons than electrons, then we have a
- positive charge.
- If we have more electrons than protons, we
- have a negative charge.
- And we know that we've defined this unit of charge called the
- coulomb, which is a bunch of the fundamental charge.
- So let's play around with this and see if
- we can measure charge.
- So part of the initial-- I guess we could call it--
- definition on what charge is, I said that like charges
- repel, right?
- Like charges repel so both of these are positive.
- They're going to repel each other.
- And unlike charges, if this is negative, this is positive,
- they're going to attract each other, right?
- So by definition, if they are moving each other, these two
- particles are going to accelerate
- away from each other.
- These two particles are going to accelerate
- towards each other.
- The charge between these particles or the charge in
- each of these particles must be generating some type of
- force, right?
- If there was no force being generated, then they wouldn't
- repel or attract each other, and this is where we get to
- Coulomb's Law, and this is why we named
- charges after Coulomb.
- Coulomb figured out that the force between two charges is
- equal to-- and this is going to be a vector quantity, and
- in about 30 seconds, I'll tell you what happens with the
- direction-- is equal to some constant times the first
- charge times the second charge divided by the distance
- between them squared.
- And this is pretty neat because this looks an awful
- lot like-- so if we call this the force, the electric force,
- that looks a lot like the gravitational force equation.
- Let me write that down.
- The force from gravity between two masses is equal to the
- gravitational constant times m1 times m2 divided by the
- distance between them squared.
- So far, the two forces that we've covered, gravity, and
- now we're covering electric force and we'll eventually
- expand this to electromagnetic force, it seems like they kind
- of act at distance in a similar way, and both of these
- forces apply in a vacuum.
- So it doesn't matter if you have no air, if you have no
- substances between the two particles, somehow they are
- communicating with each other, which I find
- kind of amazing, right?
- You can have nothing between these two particles, but
- somehow, this particle knows that that particle's there and
- that particle knows that that particle's there, and they
- start moving without having any-- it's not like they have
- a wire connected to each other and someone's telling the
- other particle, hey, there's a particle there.
- Start moving.
- So I don't know if you find that as amazing as I do, but
- think about it and you might.
- And it's just like gravity.
- I mean, the two masses are in no way connected.
- They could be sitting in a vacuum, but somehow, they know
- that the other particle's there.
- And when we start learning about special relativity and
- all of that, we'll learn that there's nothing there, but
- maybe the masses are actually somehow shaping the universe.
- And maybe that's happening with the
- electric charges as well.
- But all we know at this point is that we have these charges
- and that they exert a force on each other that's proportional
- to the product of their respective charges divided by
- the square of the distance between them.
- And this constant right here, that is-- I always forget it.
- What was it?
- I think it's 6.-- I always forget what that constant is.
- It is 9 times 10 to the ninth.
- It's rounded, of course.
- That would be amazing if it was exactly 9.
- 9 times 10 to the ninth, and the units are newton-meter
- squared per coulomb squared.
- And why are those the units?
- Well, pretty much because at the end, we have coulomb,
- coulomb, so we're going to have coulomb squared divided
- by meter squared, and we want to finish with newtons, so we
- want to cancel out the coulomb squared by putting it in the
- denominator.
- We want to cancel out the meter squared by putting it in
- the numerator, and then we'll end up with the newtons to get
- the force, so that's just where the units come from.
- So given that, let's figure out the
- force between two particles.
- So let's say I have-- and I've spent 10 minutes with a pretty
- long-winded explanation, but the actual problems you'll see
- in your physics class are pretty straightforward when it
- comes to Coulomb's Law.
- So they'll say, hey, we have a positive-- we have a particle
- here that has a positive charge of plus-- let me think
- of a good number-- plus 5 times 10 to the minus 3
- coulombs, so that's a positive charge.
- And then we have a negative charge here, so let's say
- that-- I don't know.
- How far will I make them?
- Let's say that they're half a meter apart, 0.5 meters apart,
- and then I have a negative charge here that is 10 minus
- 10 times 10 to the minus 2 coulombs.
- So what is the force between these two particles?
- So if we just plug them in to Coulomb's Law, we get the
- force due to the electricity.
- The electrical force.
- Not due to electricity.
- We haven't done that yet.
- The static electric force between those two particles is
- equal to the constant 9 times 10 to the ninth times the
- first charge times 5 times 10 to the minus 3 times the
- second charge-- let me do that in a different color-- times
- minus 10 times 10 to the minus 2-- I just rewrote that,
- although you probably can't see it-- divided by the
- distance squared, so 0.5 squared.
- We just plugged into this formula.
- So that equals-- let me see.
- So 9 times 0.5 times 10.
- I'm just going to do the 10 separately.
- So that's times minus 10.
- This is 0.5 times minus 10 is minus 5 times 9 is minus 45,
- and then 10 to the ninth minus 3, so 10 to the sixth, and
- then minus 2, so 10 to the fourth-- times 10 to the
- fourth-- divided by-- and what's 0.5 squared?
- It's 0.25, right?
- And this is equal to what?
- That's equal to 4 times this top, 160, plus this is equal
- to minus 180 times 10 to the fourth newtons.
- And actually, this might seem like a large number, but these
- charges that I put here are actually fairly large charges,
- and hopefully you'll get a sense for what's a big or a
- small charge later.
- But these are reasonably large charges, and so that's why
- there's a relatively large force exerting between these
- two particles.
- Now, we got a negative number, so what does that mean?
- Well, we know that unlike particles attract, right?
- Almost by definition.
- In this case, we had a positive and a negative, so
- when we end up with a negative force when we use Coulomb's
- Law, that means that the force will draw the two particles to
- each other along the shortest distance between them.
- I mean, it's not going to make them go in a curve.
- That kind of makes sense.
- If we had a positive there, that means that the force was
- repelling the two particles.
- And if you ever get confused, just think about it.
- If they're both negative, they're going to repel.
- If they're both positive, they're going to attract.
- I will see you in the next video.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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