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 2) Electric Fields
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- 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.
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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