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  • We're going to talk about again some new concepts.

  • And that's the concept of electrostatic potential

  • electrostatic potential energy. For which we will use the

  • symbol U and independently electric potential.

  • Which is very different, for which we will use the

  • symbol V. Imagine that I have a charge Q

  • one here and that's plus, plus charge,

  • and here I have a charge plus Q two and they have a distant,

  • they're a distance R apart. And that is point P.

  • It's very clear that in order to bring these charges at this

  • distance from each other I had to do work to

  • bring them there because they repel each other.

  • It's like pushing in a spring. If you release the spring you

  • get the energy back. If they were -- they were

  • connected with a little string, the string would be stretched,

  • take scissors, cut the string fweet they fly

  • apart again. So I have put work in there and

  • that's what we call the electrostatic potential energy.

  • So let's work this out in some detail how much work I have to

  • do. Well,

  • we first put Q one here, if space is empty,

  • this doesn't take any work to place Q one here.

  • But now I come from very far away, we always think of it as

  • infinitely far away, of course that's a little bit

  • of exaggeration, and we bring this charge Q two

  • from infinity to that point P. And I, Walter Lewin,

  • have to do work, I have to push and push and

  • push and the closer I get the harder I have to push and

  • finally I reach that point P.

  • Suppose I am here and this separation is little R.

  • I've reached that point. Then the force on me,

  • the electric force, is outwards.

  • And so I have to overcome that force and so my force F Walter

  • Lewin is in this direction. And so you can see I do

  • positive work, the force and the direction in

  • which I'm moving are in the same direction, I do positive work.

  • Now, the work that I do could be calculated.

  • The work that Walter Lewin is doing in going all the way from

  • infinity to that location P is the integral going from in-

  • infinity to radius R of the force of Walter Lewin dot DR.

  • But of course that work is exactly the same,

  • either one is fine, to take the electric force in

  • going from R to infinity.

  • Dot DR. Because the force,

  • the electric force, and Walter Lewin's force are

  • the same in magnitude but opposite direction,

  • and so by flipping over, going from infinity to R,

  • to R to infinity, this is the same.

  • This is one and the same thing. Let's calculate this integral

  • because that's a little easy. We know what the electric force

  • is, Coulomb's law, it's repelling,

  • so the force and DR are now in the same direction,

  • so the angle theta between them is zero, so the cosine of theta

  • is one, so we can forget about all the vectors,

  • and so we would get then that this equals Q one,

  • Q two, divided by four pi epsilon zero.

  • And now I have downstairs here an R squared.

  • And so I have the integral now DR divided by R squared.

  • From capital R to infinity. And this integral is minus one

  • over R.

  • Which I have to evaluate between R and infinity.

  • And when I do that that becomes plus one over capital R.

  • Right, the integral of DR over R squared I'm sure you can all

  • do that is minus one over R. I evaluate it between R and

  • infinity and so you get plus one over R.

  • And so U, which is the energy that -- the work that I have to

  • do to bring this charge at that position,

  • that U is now Q one. Times Q two divided by four pi

  • epsilon zero. Divided by that capital R.

  • And this of course this is scalar, that is work,

  • it's a number of joules. If Q one and Q two are both

  • positive or both ne- negative, I do positive work,

  • you can see that, minus times minus is plus.

  • Because then they repel each other.

  • If one is positive and the other is

  • negative, then I do negative work, and you see that that

  • comes out as a sign sensitive, minus times plus is minus,

  • so I can do negative work. If the two don't have the same

  • polarity. I want you to convince yourself

  • that if I didn't come along a straight line from all the way

  • from infinity, but I came in a very crooked

  • way, finally ended up at point P, at that point,

  • that the amount of work that I had to do is exactly the same.

  • You see the parallel with eight oh one where we dealt with

  • gravity. Gravity is a conservative force

  • and when you deal with conservative forces,

  • the work that has to be done in going from one point to the

  • other is independent of the path.

  • That is the definition of conservative force.

  • Electric forces are also conservative.

  • And so it doesn't make any difference whether I come along

  • a straight line to this point or whether I do that in an

  • extremely crooked way and finally end up here.

  • That's the same amount of work. Now if we do have a collection

  • of charges, so we have pluses and minus charges,

  • some pluses, some minus, some pluses,

  • minus, pluses, pluses, then you now can

  • calculate the amount of work that I, Walter Lewin,

  • have to do in assembling that. You bring one from infinity to

  • here, another one, another one,

  • and you add up all that work, some work may be positive,

  • some work may be negative. Finally you h- arrive at the

  • total amount of work that you have to

  • do to assemble these charges. And that is the meaning of

  • capital U. Now I turn to electric

  • potential. And for that I start off here

  • with a charge which I now call plus capital Q.

  • It's located here. And at a position P at a

  • distance R away I place a test charge plus Q.

  • Make it positive for now, you can change it later to

  • become a negative. And so the electrostatic

  • potential energy we -- we know already, we just calculated it,

  • that would be Q times Q divided by four pi epsilon zero R.

  • That's exactly the same that we have.

  • So the electric potential, electrostatic potential energy,

  • is the work that I have to do to bring this charge here.

  • Now I'm going to introduce electric potential.

  • Electric potential. And that is the work per unit

  • charge that I have to do to go from infinity to that

  • position. So Q doesn't enter into it

  • anymore. It is the work per unit charge

  • to go from infinity to that location P.

  • And so if it is the work per unit charge, that means little Q

  • fweet disappears. And so now we write down that V

  • at that location P, the potential,

  • electric potential at that location P,

  • is now only Q divided four pi epsilon zero R.

  • Little Q has disappeared. It is also a scalar.

  • This has unit joules. The units here is joules per

  • coulombs. I have divided out one charge.

  • It's work per unit charge. No one would ever call this

  • joules per coulombs, we call this volts,

  • called after the great Volta, who did a lot of research on

  • this. So we call this volts.

  • But it's the same as joules per coulombs.

  • If we have a very simple situation like we have here,

  • that we only have one charge, then this is the potential

  • anywhere, at any distance you want, from this charge.

  • If R goes up, if you're further away,

  • the potential will become lower.

  • If this Q is positive, the potential is everywhere in

  • space positive for a single charge.

  • If this Q is negative, everywhere in space the

  • potential is negative. Electro- electric static

  • potential can be negative. The work that I do per unit

  • charge coming from infinity would be negative,

  • if that's a negative charge. And the potential when I'm

  • infinitely far away, when this R becomes infinitely

  • large, is zero. So that's the way we

  • define our zero. So you can have positive

  • potentials, near positive charge, negative potentials,

  • near negative charge, and if you're very very far

  • away, then potential is zero. Let's now turn to our

  • Vandegraaff. It's a hollow sphere,

  • has a radius R. About thirty centimeters.

  • And I'm going to put on here plus ten microcoulombs.

  • It will distribute itself uniformly.

  • We will discuss that next time in detail.

  • Because it's a conductor. We already discussed last

  • lecture that the electric field inside the sphere is zero.

  • And that the electric field outside is not zero but that we

  • can think of all the charge being at this point here,

  • the plus ten microcoulombs is all here, as long as we want to

  • know what the electric field outside is.

  • So you can forget the fact that it is a -- a sphere.

  • And so now I want to know what the electric potential is at any

  • point in space. I want to know what it is here

  • and I want to know what it is here at point P which is now a

  • distance R from the center. And I want to know what it is

  • here. At a distance little R from the

  • center. So let's first do the potential

  • here. The potential at point P is

  • an integral going from R to infinity if I take the electric

  • force divided by my test charge Q dot DR, but this is the

  • electric field, see, this force times distance

  • is work, but it is work per unit charge, so I take my test charge

  • out. And so this is the integral in

  • R to infinity of E dot DL -- DR, sorry.

  • And that's a very easy integral.

  • Because we know what E is. The electric field we have done

  • several times. Follows immediately from

  • Coulomb's law and so when you calculate this integral you get

  • Q divided by four pi epsilon zero R which is no surprise

  • because we already had that for a point

  • charge. So this is the situation if R,

  • little R, is larger than capital R.

  • Precisely what we had before. We can put in some numbers.

  • If you put in R equals R, which is uh oh point three

  • meters, and you put in here the ten microcoulombs,

  • and here the -- the thirty centimeters, then you'll find

  • three hundred thousand volts.

  • So you get three times ten to the fifth volts.

  • If you um take R equals sixty centimeters, you double it,

  • if you double the distance, the potential goes down by a

  • factor of two, it's one over R,

  • so it would be a hundred and fifty kilovolts.

  • And if you go to three meters, then it is ten times smaller,

  • then it is thirty kilovolts. And if you go to infinity which

  • for all practical purposes would be

  • Lobby seven, if you go to Lobby seven,

  • then the potential for all practical purposes is about

  • zero. Because R is so large that

  • there is no potential left. So if I, if I,

  • Walter Lewin, march from infinity to this

  • surface of the Vandegraaff, and I put a charge Q in my

  • pocket, and I march to the Vandegraaff,

  • by the time I reach that point, I have done work,

  • I multiply the charge now back to the potential,

  • that gives you the work again, because potential was work per

  • unit charge, and so the work that I have done then is the

  • charge that I have in my pocket times the potential,

  • in this case the potential of the Vandegraaff.

  • If I go all the way to this surface,

  • which is three hundred thousand volts.

  • If I were a strong man then I would put one coulomb in my

  • pocket. That's a lot of charge.

  • Then I would have done three hundred thousand joules of work.

  • By just carrying the one coulomb from Lobby seven to the

  • Vandegraaff. That's about the same work I

  • have to do to climb up the Empire State Building.

  • The famous MGH, my mass times G times the

  • height that I have to climb. So I know how the

  • electric potential goes with distance.

  • It's a one over R relationship. Now I have arrived at the

  • Vandegraaff, I am at the surface, with my test charge,

  • and now I go inside. And I slosh around inside,

  • I feel no force anymore. There is no electric field

  • inside. So as I move around inside,

  • I experience no force. That means I do no work.

  • So that means that the potential

  • must remain constant. So the absence of an electric

  • field here implies that the electric potential everywhere is

  • exactly the same inside is the same as on the sphere.

  • Because no further work is needed in marching around with a

  • test charge. And so for this special case I

  • could make a graph of the electric potential versus R and

  • this is then the radius of the Vandegraaff and

  • that would be a constant all the way up to this point and

  • then it would fall off as one over R here.

  • And in for the numbers that we have chosen, the potential at

  • the maximum here would be three hundred thousand volts.

  • Just as when you look at maps where you see contours of equal

  • height of mountains, which we call equal

  • altitudes, here we have surfaces of equipotential.

  • And if you had a point charge or if you had the Vandegraaff,

  • these surfaces would be concentric spheres.

  • The further out you go, if the charge is positive,

  • the lower the potential would be.

  • They would be nicely spherical surfaces.

  • Suppose now we had more than one charge,

  • we had a plus Q one charge, and we had a minus Q two

  • charge, for instance. And you're being asked now what

  • is the potential at point P. Well, now the electric

  • potential at point P, VP, is the potential that you

  • would have measured if Q one had been there alone.

  • And you have to add the potential that you would have

  • seen if Q two had been there alone.

  • Just adding work per unit charge for one with work per

  • unit charge of the other. And if this is negative,

  • then this quantity is negative, and this is positive.

  • So when you have configurations of positive and negative charges

  • then of course depending upon where you are in space,

  • if you're close to the plus charge, the potential is almost

  • certainly positive, because the one over R is huge.

  • If you're very close to the negative charge again the one

  • over R of this little charge will dominate and so you get a

  • negative potential. And so you have surfaces of

  • positive potential and you have equipotential surfaces of

  • negative potentials and so there are surfaces which have zero

  • potential. And they're not always very

  • easy to envision. But what I want to show you is

  • some work that Maxwell himself did in

  • figuring out these equipotentials.

  • And so I have here a transparency of publication by

  • Maxwell. You see a charge,

  • let's assume it is plus four and plus one,

  • it could be minus four and minus one, but let's assume

  • they're plus. And you see the green lines,

  • which we have seen before, which are the field lines.

  • Don't pay any attention to the green field lines now.

  • The red lines are equipotentials.

  • And you have to rotate them about

  • the vertical, because they're of course

  • surfaces, this is three-dimensional.

  • I have not drawn all the equipotential surfaces in red

  • because they become too cluttered here.

  • But I've tried to put most of them in red.

  • Since this charge is positive and that charge is positive,

  • everywhere in space, no matter where you are,

  • the potential has to be positive.

  • There is not a single point where it could be negative.

  • If you are very far away from the plus four and the plus one,

  • then you expect that the equipotential surfaces are

  • spheres, because it's almost as if you were looking at a plus

  • five charge. So it doesn't surprise you that

  • when you go far out that you ultimately get spherical shapes.

  • When you're very close to the plus four they are perfect

  • spheres, when you're very close to the plus one,

  • they are perfect spheres. But then when you're sort of in

  • between, neither close to the plus four nor to the plus one,

  • they have this very funny shape.

  • It reminds me the shape of this balloon a little bit.

  • Sort of like this. You see.

  • And there is one surface which is most unusual equipotential

  • surface which here has a point where the electric field is

  • zero. It's sort of like twisting the

  • neck of a goose, you get something like this,

  • and so you have here a surface which has a point here and it is

  • exactly at that point where the electric field is

  • zero, that does not mean that the potential is zero,

  • of course not, the potential is positive here.

  • If you come with a positive charge from the Lobby seven and

  • you have to march up to that point, you have to do positive

  • work. You have to overcome both the

  • repelling force from the plus four and the repelling force

  • from the plus one. But finally when you reach that

  • point you can rest because there is no force on you at that

  • point. That's what it means that the

  • electric field is zero. It does not mean that you

  • haven't done any work. So never confuse electric

  • fields with potentials. I want to draw your attention

  • to the fact that the green lines, the field lines,

  • are everywhere perpendicular to the equipotentials.

  • I will get back to that during my next lecture.

  • That is not an accident. That is always the case.

  • Now, Maxwell shows you something that is a little bit

  • more complicated. Here, he calculated for us the

  • equipotential surfaces, the red ones are the surfaces,

  • again you have to rotate them about the vertical to make it

  • three-dimensional, and now we have a minus one

  • charge and a plus four. And so whenever it is red,

  • the surface, the potential is positive,

  • and whenever I have drawn it blue, the potential is negative.

  • First, if we were very far away from both the plus four and the

  • minus one, you expect to be looking at a charge which is

  • effectively plus three. And so if you go very far away

  • for sure the potential is

  • everywhere positive and you expect them to be spherical

  • again. If you look here you're very

  • far away from the plus four and the minus one,

  • indeed this has already the shape of a sphere.

  • So that's clear that the plus four and the minus one far away

  • behave like a plus three. If you're very close to the

  • plus four, you get nice spheres around the plus four,

  • positive potential, if you're very close to the

  • minus one, notice that the blue surfaces are almost nice

  • spheres, but now they're all negative because you're very

  • close to the minus one. So a negative potential.

  • There is here one surface which now has zero potential.

  • It has to be because if you're negative potential close to the

  • minus one and you have positive potential very far out,

  • you got to go through a surface where it's zero.

  • And so there is here a surface, I still have put it in blue,

  • which is actually everywhere on this surface the potential is

  • zero. Is the electric field zero

  • there? Absolutely not.

  • Electric field should not be confused with potential.

  • What it means is that if you take a test charge in your

  • pocket and you come from infinity and you walk to that

  • surface, that by the time you have reached that surface,

  • you've done zero work. That's what it means.

  • That the potential is zero.

  • There is here one point which we discussed earlier in my

  • lectures where the electric field is zero.

  • The potential is not zero there.

  • The potential is definitely positive here.

  • Because here was the zero surface.

  • Here is already positive surface, and this is a positive

  • surface. So the potential is positive.

  • However, if you reach that point there's no force on your

  • charge. So that means electric field is

  • zero. And it's not so easy of course

  • to calculate these surfaces. Maxwell was capable of doing

  • that a hundred ten years ago. And nowadays we can do that

  • very easily with computers. Equipotential surfaces which

  • have different values can never intersect.

  • Plus five volt surface can never intersect with a plus

  • three or a minus one. And you think about why that

  • is. Why that is,

  • that would be a total violation of the conservation

  • of energy. So equipotential surfaces,

  • different values, can never intersect.

  • All right. So you've seen that for the

  • various charge configurations, the equipotential surfaces have

  • very complicated shapes and cannot always be calculated in a

  • very easy way. Now comes the question why do

  • we introduce electric potentials,

  • who needs them? And who needs equipotential

  • surfaces? Isn't it true that if we know

  • the electric field vectors everywhere in space that that

  • determines uniquely how charges will move, what acceleration

  • they will obtain, that means how their kinetic

  • energy will change, and the answer is yeah,

  • if you know the electric field everywhere in space sure.

  • Then you can predict everything that happens with a charge in

  • that field. But there are examples where

  • the electric fields are so incredibly complicated that it

  • is easier to work with equipotentials because the

  • change in kinetic energy as I will discuss now really depends

  • only on the change in the potential when you go from one

  • point to another. So you will see very shortly

  • that sometimes if you're only interested in change of kinetic

  • energy and not necessarily interested in the details of the

  • trajectory, then equipotentials come in very

  • handy. Never confuse U which is

  • electrostatic potential energy with V which is electric

  • potential. This has unit joules.

  • And this has unit joules per coulombs, which we call volts.

  • If I have a collection of charges, pluses and minuses,

  • U has only one value. It is the work that I have to

  • do to put all these crazy charges exactly where they are.

  • But the electric potential is different here from there from

  • there to there to there to there.

  • If you're very close to a plus charge, you can be sure that the

  • potential is positive. If you're very close to a -- a

  • negative charge, you can be sure that the

  • potential is negative. But U has only one number.

  • It's only one value. They're both scalars.

  • Don't confuse one with the other.

  • In a gravitational field, matter, like a piece of chalk,

  • wants to go from high potential to low potential.

  • If I just release it with zero speed, there it goes,

  • high potential to low potential.

  • In analogy, positive charges will also go from a high

  • electric potential to a low electric potential.

  • And of course this is unique for electricity,

  • negative charges will go from a low potential to a high electric

  • potential. Suppose I had a position A in

  • space and I had another position B

  • and I specify the potentials. So here we have A,

  • potential is VA, and here we have point B where

  • the potential is VB. By definition,

  • the potential of VA as we discussed before is

  • the integral -- by the way if these are separated by some

  • random distance R, whatever you want.

  • So the potential of A is defined as the integral going

  • from A to infinity of E dot DR. That is the definition of the

  • potential of A. There is an E here which is

  • force per unit charge. So it is not work.

  • If there were force DR it would be work but it is force per unit

  • charge that makes it E. So the potential of B for

  • definition is the integral from B to infinity of E dot DR.

  • And so therefore the potential difference between point A and

  • B, VA minus VB, equals the integral from A to B

  • of E dot DR, and for reasons that I still don't understand

  • after having been in this business for a long time,

  • books will always tell you they reverse VA and B so they give

  • you VB, VB minus VA. And then they say well we have

  • to put a minus sign in front of the uh integral.

  • It's the same thing. So books always give it to you

  • in this form. But it is exactly the same.

  • Hope you realize that. This is the two equations that

  • I have here are the same. VA minus VB is the integral

  • from A to B of E dot DR. If I flip this over then all I

  • have to do is put a minus sign here and the two are identical.

  • Notice that if there is no electric field between A and B

  • they have the same potential, of course.

  • Because when you march from A to B with a charge in your

  • pocket no work is done. So the potential remains the

  • same. I will change this DR to a

  • different symbol, which I call DL.

  • DR would mean that we go from A to

  • infinity along this straight line and then we go from B to

  • infinity along the straight line but it makes no difference how

  • you go. If you go from A to B this

  • potential difference and you go in this way then VA minus VB is

  • not going to change. And so if now I introduce here

  • a element DL, which is a small vector,

  • and if the local E vector here is like so, at this point here,

  • then VA minus VB is then the integral of E dot DL.

  • In other words I can replace the R by an L and you may choose

  • any path that you prefer. And that's the way that we will

  • show you this equation most of the time.

  • So it makes no difference how you

  • march because we are dealing here with conservative fields.

  • So let's now make the assumption that VA is a hundred

  • fifty volts. And that VB for instance is

  • fifty volts. So it's a very specific

  • example. What does it mean now?

  • It means that if I put plus Q charge in my pocket and I come

  • all the way from Lobby seven and I walk up to point B.

  • So Walter Lewin plus Q charge in his pocket goes from Lobby

  • seven to point B, I have to do work and the work

  • I have to do is the product of my charge Q with the potential.

  • So that is Q the work I have to do is Q times VB.

  • So in this case it's fifty times Q, whatever that charge is

  • that I have in my pocket. This

  • is in joules. Now, I go from Lobby seven to

  • point A. I have to do more work.

  • I have to do a hundred fifty Q joules of work.

  • You can think of it I first come to A to B,

  • I'm already exhausted, I have to put in another work

  • to get all the way to point A. So you can imagine if I have

  • this plus Q charge at point A, where there it's it's a higher

  • potential, it wants to go back all by itself to B.

  • It wants to go from a higher potential to a lower potential.

  • Look, the E vector is in this direction.

  • Positive charge will go to a lower potential.

  • And as it moves from A to B energy is released.

  • How much energy? Well, this is the amount of

  • work I have done to get to A, this is the amount of work I

  • did to get to B, and so if now the charge goes

  • back from A to B, it's the difference that

  • becomes available in terms of kinetic energy.

  • It's a change in potential energy.

  • And that change in potential energy, so the change in

  • potential energy, when the plus Q charge goes

  • from A to B, that change is Q times VA minus VB.

  • QVB at point B and QVA at point A.

  • So this is the potential energy that is in principle available

  • if the charge moves from A to B. And you remember from eight oh

  • one the work energy theorem. If we deal with conservative

  • forces, then the sum of potential energy and kinetic

  • energy of an object is the same. That's also true for

  • gravitational forces. In other words,

  • this difference in potential energy that becomes available

  • like potential energy becomes available when I drop my chalk

  • from a high potential to a low potential,

  • that's converted to kinetic energy.

  • So this difference now is also converted into kinetic energy of

  • that moving charge. And so that would be the

  • kinetic energy at point B minus the kinetic energy at point A.

  • Which is really the work energy theorem.

  • It's the conservation of energy.

  • Now any piece of metal, no matter how crumby or dented

  • it is, is an equipotential. As long as there is no charge

  • moving inside the metal. And that's obvious that it's an

  • equipotential. Because these charges inside

  • the metal, these electrons, when they experience an

  • electric field, they begin to move immediately

  • in the electric field, and they will move until there

  • is no force on them anymore, and that means they have

  • effectively made the electric field zero.

  • So charges inside the conductor always move automatically in

  • such a way that they kill the electric

  • field inside. If the electric field hadn't

  • been zero yet, they would still be moving.

  • And so each metal that you have, no matter where you bring

  • it, as long as there are no electric currents inside,

  • will always be an equipotential.

  • So I can take a trash can and bring it into an external field

  • and then very shortly after I've brought it in when things have

  • calmed down, the trash can will be an

  • equipotential and the electric field inside the metal will

  • everywhere will everywhere be zero.

  • So I could for instance attach point A to a trash can,

  • metal trash can, so the whole trash can would be

  • at a hundred fifty volts, and I could put point B,

  • make it part of my -- of my soda, which is also made of

  • metal. And so the whole soda would be

  • at fifty volts and the entire trash can

  • would be at a hundred fifty volts.

  • I place the whole thing in vacuum and now I release an

  • electron at point B. An electron.

  • An electron wants to go to higher potential.

  • A proton would go from A to B, electron wants to go from B to

  • A. And so now energy is available.

  • The electric potential energy is available and the electron

  • will start to pick up speed and

  • finally end up at A. Now how it will travel I don't

  • know. The electric field

  • configuration is enormously complicated.

  • Between the can and this trash can.

  • Amazingly complicated. If you were to see the field

  • lines it would be weird. But if we all we want to know

  • is what the kinetic energy is, what the speed is,

  • with which this electron reaches the can,

  • so what? Then we can use the work

  • energy theorem and find out immediately what that kinetic

  • energy is. Because the available potential

  • energy is the charge of the electron times the potential

  • difference between these two objects.

  • Well the charge of the electron is one point six times ten to

  • the minus nineteen coulombs. The potential difference is a

  • hundred volts. And that is the difference in

  • kinetic energy. If I assume that I release the

  • electron at zero speed, then I have immediately the

  • kinetic energy that it has at point A which is one-half M of

  • the electron times the speed at A squared.

  • So now you see that accepting the fact that we know the

  • equipotentials, we can very quickly calculate

  • the kinetic energy and therefore the speed of the electron,

  • as they arrive at A, without any knowledge of the

  • complicated electric field. If you put in the numbers for

  • the mass of the electron, then, which is nine times ten

  • to the minus thirty-one kilograms, then you'll find that

  • this speed is about two percent of the speed of light.

  • A substantial speed. All our potentials,

  • electric potentials, are defined relative to

  • infinity. That means at infinity they are

  • zero. That is because of the one over

  • R relationship. That's very nice and dandy and

  • it works. However, there are situations

  • whereby it really doesn't matter where you think of your zero.

  • Remember with gravity we had a similar situation.

  • With gravity we always worried about difference in potential

  • energy but sometimes we call this zero and this plus.

  • Sometimes you call this plus and this minus.

  • It doesn't really matter because the change in kinetic

  • energy is dictated only by the difference

  • in potentials. So it is very nice and dandy to

  • call that a hundred fifty and to call that fifty but you wouldn't

  • have found any different answer for the electron if you called

  • this potential one hundred volts and you called this one zero or

  • you called this one zero and this one minus one hundred or

  • you called this one fifty and this one minus fifty.

  • So the behavior of the electrons of the charges would

  • of course not change. And of course electrical

  • engineers would always per definition call the potential of

  • the earth zero when they built their circuits.

  • So now I would like to demonstrate to you with the

  • Vandegraaff that if you get a strong electric field from the

  • radially outwards from the Vandegraaff that you get a huge

  • potential difference between this point here and this point

  • there. Uh if I have my numbers still

  • there, I hope I do,

  • there they are, at the surface of the

  • Vandegraaff which takes about ten microcoulombs,

  • it will be three hundred thousand volts right here,

  • here it would be a hundred fifty thousand volts,

  • and here three meters from the center, it's about thirty

  • kilovolts. So that means that if I place

  • this fluorescent tube into that electric field that there would

  • be a gigantic potential difference between here and

  • there provided that I hold it radially.

  • If I hold it like this then the potential difference

  • between here and there would be zero of course,

  • if I hold it tangentially, they would be both at the same

  • electric potential. But when I hold them radially

  • you will see perhaps that this fluorescent tube will show a

  • little bit of light. Once you see light it means

  • that electrons are moving through that gas.

  • It means charge is moving. We haven't discussed current

  • yet, but that's what it means.

  • A current is flowing. And this current has to be

  • delivered by the Vandegraaff and the Vandegraaff is only capable

  • of providing very modest currents.

  • So you're not going to see a lot of light.

  • But I want to show you that you will see some light.

  • No wires attached. Just here.

  • And then I will rotate it tangentially and you will see no

  • light at all. So if we can make it a little

  • darker as a start and I'll start the

  • Vandegraaff and then if Marcos comes to make it completely dark

  • when necessary, because the light is so little

  • that we really have to make it completely dark.

  • I will put on a glove for safety reasons although I don't

  • think it will do me much good. Notice I have here a piece of

  • glass to well, to be well-insulated from the

  • glass so that I don't mess up the

  • demonstration by if I hold my fingers here it will be very

  • different than holding my hands here.

  • So let's go first close without -- with the lights still on and

  • then OK why don't you turn the lights off now all the way off.

  • OK I -- I think you can see a glow.

  • It's radially outwards now. And Marcos can you give a

  • little light? OK I will now go tangential,

  • can you turn uh the lights off? And now you see nothing,

  • very little. And now I go radial again.

  • And there you go. Now if I -- if I'm crazy,

  • if I were crazy, then I would touch the end of

  • this tube with my finger thereby allowing this current to go

  • straight through my body to the earth which may increase the

  • light. Let me try that.

  • So -- so I'm going to touch the -- the --

  • the -- this -- this fluorescent tube on your right side.

  • Ah. Ah.

  • Ah. Every time I -- I touch it ah.

  • But that's not ah. But you see every time I touch

  • it I make it easier for the current to flow and you see very

  • clearly that it lights up. Now I want to do the same

  • demonstration with a neon flash tube and the neon flash

  • tube I will place at the end of a fishing rod.

  • This neon flash tube we used during the first lecture when I

  • was beating up students but I've learned not to do that anymore.

  • Um this takes um several kilovolts to get a little bit of

  • light out of it from one side to the other, oh,

  • that's duck soup for the Vandegraaff, you know you're

  • talking about hundreds and thousands of volts,

  • and so here I will actually start spinning it and then when

  • it is radially inwards maybe you will see light and when it

  • is tangential you won't see much light and then if I feel very

  • good I will do that again. OK uh so Marcos if you make it

  • uh dark I'll give it a twist. OK, radial, radial,

  • radial, radial, radial,

  • radial, radial, radial, radial,

  • OK. Now I ah OK I touched it now I

  • touch it again. And I touch it again.

  • And again. And again.

  • Ah. You see every time I touch it

  • it lights me. And it gives a nice flash of

  • light. So you see here in front of

  • your eyes without any wires attached

  • that the potential difference created by the electric field

  • that those potential differences make these lights work.

  • All right, see you Friday.

We're going to talk about again some new concepts.

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