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  • Prof: So, I've got to start by telling

  • you the syllabus for this term--not the detailed one,

  • just the big game plan.

  • The game plan is: we will do electromagnetic

  • theory.

  • Electromagnetism is a new force that I will introduce to you and

  • go through all the details.

  • And I will do optics, and optics is part of

  • electromagnetism.

  • And then near the end we will do quantum mechanics.

  • Now, quantum mechanics is not like a new force.

  • It's a whole different ball game.

  • It's not about what forces are acting on this or that object

  • that make it move, or change its path.

  • The question there is: should we be even thinking

  • about trajectories?

  • Should we be even thinking about particles going on any

  • trajectory?

  • Forget about what the right trajectory is.

  • And you will find out that most of the cherished ideas get

  • destroyed.

  • But the good news is that you need quantum mechanics only to

  • study very tiny things like atoms or molecules.

  • Of course the big question is, you know, where do you draw the

  • line?

  • How small is small?

  • Some people even ask me, "Do you need quantum

  • mechanics to describe the human brain?"

  • And the answer is, "Yes, if it is small

  • enough."

  • So, I've gone to parties where after a few minutes of talking

  • to a person I'm thinking, "Okay, this person's brain

  • needs a fully quantum mechanical treatment."

  • But most of the time everything macroscopic you can describe the

  • way you do with Newtonian mechanics, electrodynamics.

  • You don't need quantum theory.

  • All right, so now we'll start with the brand new force of

  • electromagnetism.

  • But before doing the force, I've got to remind you people

  • of certain things I expect you all to understand about the

  • dynamics between force, and mass, and acceleration that

  • you must have learned last term.

  • I don't want to take any chances.

  • I'm going to start by reminding you how we use this famous

  • equation of Newton.

  • So you've seen this equation, probably,

  • in high school, but it's a lot more subtle than

  • you think, certainly a lot more subtle

  • than I thought when I first learned it.

  • So I will tell you what I figured out over these years on

  • different ways to look at F = ma.

  • In other words, if you have the equation what's

  • it good for?

  • The only thing anybody knows right away is a stands

  • for acceleration, and we all know how to measure

  • it.

  • By the way, anytime I write any symbol on the board you should

  • be able to tell me how you'd measure it,

  • otherwise you don't know what you're talking about as a

  • physicist.

  • Acceleration, I think I won't spend too much

  • time on how you measure it.

  • You should know what instruments you will need.

  • So I will remind you that if you have a meter stick,

  • or many meter sticks and clocks you can follow the body as it

  • moves.

  • You can find its position now, its position later,

  • take the difference, divide by the time,

  • you get velocity.

  • Then find the velocity now, find the velocity later,

  • take the difference, divide by time,

  • you've got acceleration.

  • So acceleration really requires three measurements,

  • two for each velocity, but we talk of acceleration

  • right now because you can make those three measurements

  • arbitrarily near each other, and in the limit in which the

  • time difference between them goes to zero you can talk about

  • the velocity right now and acceleration right now.

  • But in your car, the needle points at 60 that's

  • your velocity right now.

  • It's an instantaneous quantity.

  • And if you step on the gas you feel this push.

  • That's your acceleration right now.

  • That's a property of that instant.

  • So we know acceleration, but the question is can I use

  • the equation to find the mass of anything.

  • Now, very often when I pose the question the answer given is,

  • you know, go to a scale, a weighing machine,

  • and find the mass.

  • And as you know, that's not the correct answer

  • because the weight of an object is related to being near the

  • earth due to gravity, but the mass of an object is

  • defined anywhere.

  • So here's one way you can do it.

  • Now you might say, "Well, take a known force and find the

  • acceleration it produces," but we haven't talked about how

  • to measure the force either.

  • All you have is this equation.

  • The correct thing to do is to buy yourself a spring and go to

  • the Bureau of Standards and tell them to loan you a block of some

  • material, I forgot what it is.

  • That's called a kilogram.

  • That is a kilogram by definition.

  • There is no God-given way to define mass.

  • You pick a random entity and say that's a kilogram.

  • So that's not right and that's not wrong.

  • That's what a kilogram is.

  • So you bring that kilogram, you hook it up on the spring,

  • and you pull it by some amount, maybe to that position,

  • and you release it.

  • You notice the acceleration of the 1 kilogram,

  • and the mass of the thing is just one.

  • Then you detach that mass.

  • Then you ask--Then the person says, "What's the mass of

  • something else?"

  • I don't know what the something else is.

  • Let's say a potato.

  • And you take the potato or anything, elephant.

  • Here's a potato.

  • You pull that guy by the same distance, and you release that,

  • and you find its acceleration.

  • Since you pulled it by the same amount, the force is the same,

  • whatever it is.

  • We don't know what it is, but it's the same.

  • Therefore we know the acceleration of 1 kilogram times

  • 1 kilogram is equal to the unknown mass times the

  • acceleration of the unknown mass.

  • That's how by measuring this you can find what the mass is.

  • In principle you can find the mass of everything.

  • So imagine masses of all objects have been determined by

  • this process.

  • Then you can also use F = ma to find out what forces

  • are acting on bodies in different situations,

  • because if you don't know what force is acting on a body you

  • cannot predict anything.

  • So you can go back to the spring and say,

  • "I want to know what force the spring exerts when it's

  • pulled by various amounts.

  • Well, you pull it by some amount x.

  • You attach it to a non-mass and you find the acceleration,

  • and that's the force.

  • And if you plot it, you'll find F as a

  • function of x will be roughly a straight line and it

  • will take the form F = -kx,

  • and that k is called a force constant.

  • So this is an example of your finding out the left hand side

  • of Newton's law.

  • You've got to understand the distinction between F =

  • -kx and F = ma.

  • What's the difference?

  • This says if you know the force I can tell you the acceleration,

  • but it's your job to go find out every time what forces might

  • be acting on a body.

  • If it's connected to a spring, and you pull the spring and it

  • exerts a force, someone's got to make this

  • measurement to find out what the force will be.

  • All right, so that's one kind of force.

  • Another force that you can find is if you're near the surface of

  • the earth, if you drop something,

  • it seems to accelerate towards the ground,

  • and everything accelerates by the same amount g.

  • Well, according to Newton's laws if anything is going to

  • accelerate, it's because there's a force on it.

  • The force on any mass m must be mg,

  • because if I divide by m I've got to get g.

  • So the force on masses near the earth is mg.

  • That's another force.

  • Something interesting about that force is that unlike the

  • spring force where the spring is touching the mass,

  • you can see it's pulling it, or when I push this chair you

  • can see I'm doing it, the pull of gravity is a bit

  • strange, because there is no real

  • contact between the earth and the object that's falling.

  • It was a great abstraction to believe that things can reach

  • out and pull things which are not touching them,

  • and gravity was the first formally described force where

  • that was true.

  • And another excursion in the same theme is if this object

  • gets very far, say like the moon over there,

  • then the force is not given by mg,

  • but the force is given by this law of gravitation.

  • For every r near the surface of the earth,

  • if you put r equal to the surface of the earth you

  • will get a constant force that is just mg,

  • but if you move far from the center of the earth you've got

  • to take that into account, and that's what Newton did and

  • realized the force goes like 1 over r^(2).

  • So every time things accelerate you've got to find the reason,

  • and that reason is the force.

  • Many times many forces can be acting on a body,

  • and if you put all the forces that are acting on a body and

  • that explains the acceleration, you're done,

  • but sometimes it won't.

  • That's when you have a new force.

  • And the final application of F = ma is this one.

  • If you knew the force, for example,

  • on a planet, and here's a planet going

  • around the sun and it is here.

  • This is the sun, and you know the force acting

  • on it given by Newton's Law of Gravity you can find the

  • acceleration that will help you find out where it will be one

  • second later, and you repeat the calculation,

  • you will get the trajectory.

  • So F = ma is good for three things,

  • that's what I want you to understand: to define mass,

  • to calculate forces acting on bodies by seeing how they

  • accelerate, and finally to find the

  • acceleration of bodies given the forces.

  • This is the cycle of Newtonian dynamics.

  • And what I'm going to do now is to add one more new force,

  • because I'm going to find out that there is another force not

  • listed here.

  • I'm going to demonstrate to you that new force,

  • okay?

  • Here's my demonstration.

  • The only demonstration you will see in my class,

  • because everything else I've tried generally failed,

  • but this one always works.

  • So, I have here a piece of paper, okay?

  • Then I take this trusty comb and I comb the part of my head

  • that's suited for this experiment,

  • then I bring it next to this, and you see I'm able to lift

  • that.

  • Now, that's not the force of gravity because gravity doesn't

  • care if you comb your hair or not, okay?

  • And also when I shake it, it falls down.

  • So you're thinking, "Okay, maybe there is a new force but

  • it doesn't look awfully strong because it's not able to even

  • overcome gravity, because it eventually yielded

  • to gravity and fell down," but it's actually a mistake to

  • think so.

  • In fact this new force that I'm talking about is 10 to the power

  • of 40 stronger than gravitational force.

  • I will tell you by what metric I came up with that number,

  • but it's an enormously strong force.

  • You've got to understand why I say it is such a strong force

  • when, when I shook it the thing fell down.

  • So the reason is that if you look at this experiment,

  • here's the comb and here's the paper,

  • the comb is trying to pull the paper,

  • but what is trying to pull it down?

  • What is trying to pull it down?

  • So here is me, here is that comb,

  • here's the paper.

  • The entire planet is pulling it down: Himalayas pulling it down,

  • Pacific Ocean, pulling it down,

  • Bin Laden sitting in his cave pulling it down.

  • Everything is pulling it down, okay?

  • I am one of these people generally convinced the world is

  • acting against me, but this time I'm right.

  • Everything is acting against me, and I'm able to triumph

  • against all of that with this tiny comb.

  • And that is how you compare the electric force with the