Kelistrikan dan Kemagnetan

**Topics covered:**

Electric Field

Field Lines

Superposition

Inductive Charging

Dipoles

Induced Dipoles

**Instructor/speaker:** Prof. Walter Lewin

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Today I'm going to work with you on a new concept and that is the concept of what we call electric field.

We spend the whole lecture on electric fields.

If I have a -- a charge, I just choose Q, capital Q and plus at a particular location and at another location I have another charge little Q, I think of that as my test charge.

And there is a separation between the two which is R.

The unit vector from capital Q to li- little Q is this vector.

And so now I know that the two charges if they were positive -- let's suppose that little Q is positive, they would repel each other.

Little Q is negative they would attract each other.

And let this force be F and last time we introduced Coulomb's law that force equals little Q times capital Q times Coulomb's constant divided by R squared in the direction of R roof.

The two have the same sign.

It's in this direction.

If they have opposite sign it's in the other direction.

And now I introduce the idea of electric field for which we write the symbol capital E.

And capital E at that location P where I have my test charge little Q, at that location P is simply the force that a test charge experienced divided by that test charge.

So I eliminate the test charge.

So I get something that looks quite similar but it doesn't have the little Q in it anymore.

And it is also a vector.

And by convention, we choose the force such that if this is a positive test charge then we say the E field is away from Q if Q is positive, if Q is negative the force is in the other direction, and therefore E is in the other direction.

So we adopt the convention that the E field is always in the direction that the force is on a positive test charge.

What you have gained now is that you have taken out the little Q.

In other words, the force here depends on little Q.

Electric field does not.

The electric field is a representation for what happens around the charge plus Q.

This could be a very complicated charge configuration.

An electric field tells you something about that charge configuration.

The unit for electric field you can see is newtons divided by coulombs.

In SI units and normally we won't even indicate the-- the unit, we just leave that as it is.

Now we have graphical representations for the electric field.

Electric field is a vector.

So you expect arrows and I have here an example of a -- a charge plus three.

So by convention the arrows are pointing away from the charge in the same direction that a positive test charge would experience the force.

And you notice that very close to the charge the arrows are larger than farther away.

That it, that sort of represents- is trying to represent- the inverse R square relationship.

Of course it cannot be very qualitative.

But the basic idea is this is of course spherically symmetric, if this is a point charge.

The basic idea is here you see the field vectors and the direction of the arrow tells you in which direction the force would be, if it is a positive test charge.

And the length of the vector give you an idea of the magnitude.

And here I have another charge minus one.

Doesn't matter whether it is minus one coulomb or minus microcoulomb.

Just it's a relative representation.

And you see now that the E field vectors are reversed in direction.

They're pointing towards the minus charge by convention.

And when you go further out they are smaller and you have to go all the way to infinity of course for the field to become zero.

Because the one over R square field falls off and you have to be infinitely far away for you to not experience at least in principle any effect from the..

from the charge.

What do we do now when we have more than one charge?

Well, if we have several charges -- here we have Q one, and here we have Q two, and here we have Q three, and let's say here we have Q of i, we have i charges.

And now we want to know what is the electric field at point P.

So it's independent of the test charge that I put here.

You can think of it if you want to as the the force per unit charge.

You've divided out the charge.

So now I can say what is the E field due to Q one alone?

Well, that would be if Q one were positive then this might be a representation for E one.

If Q two were negative, this might be a representation for E two, pointing towards the negative charge.

And if this one were negative, then I would have here a contribution E three, and so on.

And now we use the superposition principle as we did last time with Coulomb's law, that the net electric field at point P as a vector is E one in reference of charge Q one, plus the vector E two, plus E three, and so on and if you have i charges, it is the sum of all i charges of the individual E vectors.

Is it obvious that the superposition principle works?

No.

Does it work?

Yes.

How do we know it works?

Because it's consistent with all our experimental results.

So we take the superposition principle for granted and that is acceptable.

But it's not obvious.

If you tell me what the electric field at this point is, which is the vectorial sum of the individual E field vectors, then I can always tell you what the force will be if I bring a charge at that location.

I take any charge that I always would carry in my pocket, I take it out of my pocket and I put it at that location.

And the charge that I have in my pocket is little Q.

Then the force on that charge is always Q times E.

Doesn't matter whether Q is positive, then it will be in the same direction as E.

If it is negative it will be in the opposite direction as E.

If Q is large the force will be large.

If Q is small the force will be small.

So once you know the E field it could be the result of very complicated charge configurations.

The real secret behind the concept of an E field is that you bring any charge at that location and you know what force acts at that point on that charge.

If we try to be a little bit more quantitative, suppose I had here a charge plus three and here I had a charge minus one.

Here's minus one.

And I want to know what the field configuration is as a result of these two charges.

So you can go to any particular point.

You get an E vector which is going away from the plus three, you get one that goes to minus one, and you have to vectorially add the two.

If you are very close to minus one, it's very clear because of the inverse R square relationship that the minus one is probably going to win.

Let's in our mind take a plus test charge now.

And we put a plus test charge very close to minus one, say put it here, even though plus three is trying to push it out, clearly minus one is most likely to win.

And so there will probably be a force on my test charge in this direction.

The net result of the effects of the two.

Suppose I take the same positive test charge and I put it here, very far away, much farther away than this separation.

What do you think now is the direction of the force on my plus charge?

Very far away.

Excuse me.

Why do you think it's to the left?

Do you think minus one wins?

A: [inaudible].

Do you really think the minus one is stronger than the plus three because the plus three will push it out and the minus one tries to lure it in, right, if the test charge is positive.

A: [inaudible] plus two.

So if you're far away from a configuration like this, even if you were here, or if you were there, or if you're way there, clearly the field is like a plus two charge.

And falls off as one over R squared.

So therefore, if you're far away the force is in this direction.

And now look, what is very interesting.

Here if you're close to the minus one, the force is in this direction.

Here when you're very far away, maybe I should be all the way here, it's in that direction.

So that means there must be somewhere here the point where the E field is zero.

Because if the force is here in this direction but ultimately turns over in that direction, there must be somewhere a point where E is zero.

And that is part of your assignment.

I want you to find that point for a particular charge configuration.

So let's now go to-- some graphical representations of a situation which is actually plus three minus one.

Try to improve on the light situation.

And let's see how these electric vectors, how they show up in the vicinity of these two charges.

So here you see the plus three and the minus one, relative units, and let's take a look at this in some detail.

First of all the length of the arrows again indicates the strength.

It gives you a feeling for the strength.

It's not very quantitative of course.

And so let's first look at the plus three, which is very powerful.

You see that these arrows all go away from the plus three and when you're closer to the plus three, they're stronger, which is a representation of the inverse R square field.

If you're very close to the minus one, ah the arrows are pointing in towards the minus one, because the one over R square, the minus one wins.

And so you see they're clearly going into the direction of the minus one.

Well, if you're in between the plus and the minus on this line, always the E field will be pointing from the plus to the minus.

Because the plus is pushing out and the minus is sucking in.

So the two support each other.

But now if you go very far away from this charge configuration, anywhere but very far away, much farther than the distance between the two charges, so somewhere here, or somewhere there, or somewhere there, or here, notice that always the arrows are pointing away.

And the reason is that plus three and minus one is as good as a plus two if you're very very far away.

But of course when you're very close in, then the field configuration can be very, very complicated.

But you see very clearly that these arrows are all pointing outwards.

None of them come back to the minus one.

None of them point to the minus one direction.

And that's because the plus three is more powerful and then there is here this point and only one point whereby the electric field is zero.

If you put a positive test charge here, the minus will attract it, the plus will repel it, and therefore there comes a point where the two cancel each other exactly.

Now there is another way of electric field representation which is more organized.

And we call these field lines.

So you see again the plus three and you see there the minus one.

If I release right here or I place here a positive test charge, all I know is that the force will be tangential to the field lines.

That is the meaning of these lines.

So if I'm here, the force will be in this direction.

If I put a positive test charge here, the force will be in this direction, and of course, if it's a negative charge the force flips over.

So the meaning of the field lines are that it always tells you in which direction a charge experiences a force.

A force a positive charge always in the direction of the arrows, tangentially to the field lines and a negative charge in the opposite direction.

How many field lines are there in space?

Well of course there are an infinite number.

Just like these little arrows that we had before, we only sprinkled in a few but of course in every single point there is an electric field and so you can put in an infinite number of field lines and that would make this a representation of course useless.

So we always limit ourselves to a certain number.

If you look very close to the minus one, notice that all the field lines come in on the minus one.

We understand that of course because a positive charge would want to go to the minus one.

If you're very close to the plus and they all go away from the plus because they're being repelled...

You can sort of think as these field lines if you want to imagine the configuration that the plus charges blow out air like a hairdryer, and that the minus suck in air like a vacuum cleaner, and then you get a feeling for there is on this left side here this hairdryer which wants to blow out stuff and then there is that little sucker that wants to suck something in and it succeeds to some degree, it's not as powerful as the plus three, though.

Have we lost all information about field strength?

We had earlier with these arrows, we had the length of the arrow, the magnitude of the field was represented.

Yeah, you have lost that, but there is still some information on field strength.

If the lines are closer together, if the density of the lines is high, the electric field is stronger than when the density becomes low.

So if you look for instance here, look how many lines there are per few millimeters, and when you go further out these lines spread out, that tells you the E field is going down, the strength of the E field is going down.

It's the one over R square field of course.

If you want to make these drawings what you could do to make them look good, you can make three times more field lines going out from the plus in this case than return to the minus one.

So the field lines are very powerful and we will often think in terms of electric fields and the line configurations and you will have several homework problems that deal with electric fields and with the electric field lines.

If an electric field line is straight, so I have electric fields, get some red chalk, say we have fields that are like this, straight E field lines, and I release a charge there, for instance a positive charge, then the positive charge would experience a force exactly in the same direction as the field lines, because the tangential now is in the direction of the field line, it would become accelerated in this direction and would always stay on the field lines.

If I release it with zero speed, start to accelerate and it would stay on the field lines.

In a similar way, if we think of the earth as having a gravitational field, with eight o one we may never have used that word, gravitational field, but in physics we think of the -- of gravity of also being a field.

If I have here a piece of chalk the-- the field lines, the gravitational field lines, here in twenty-six one hundred, nicely parallel and straight and if I release this piece of chalk at zero speed it will begin to move in the direction of the field lines, and it will stay on the field lines.

So now you can ask yourself the question if I release a charge would it always follow the field lines?

And the answer is no.

Only in this very special case.

Pengembangan Perkuliahan

1. Buatlah sebuah Esai mengenai materi perkuliahan ini

2. Buatlah sebuah kelompok berjumlah 5 orang untuk menganalisis materi perkuliahan ini

3. Lakukan Penelitian Sederhana dengan kelompok tersebut

4. Hasilkan sebuah produk yang dapat digunakan oleh masyarakat

5. Kembangkan produk tersebut dengan senantiasa meningkatkan kualitasnya#### Staff

Visualizations:

Prof. John Belcher

Instructors:

Dr. Peter Dourmashkin

Prof. Bruce Knuteson

Prof. Gunther Roland

Prof. Bolek Wyslouch

Dr. Brian Wecht

Prof. Eric Katsavounidis

Prof. Robert Simcoe

Prof. Joseph Formaggio

Course Co-Administrators:

Dr. Peter Dourmashkin

Prof. Robert Redwine

Technical Instructors:

Andy Neely

Matthew Strafuss

Course Material:

Dr. Peter Dourmashkin

Prof. Eric Hudson

Dr. Sen-Ben Liao

#### Acknowledgements

The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation. Many people have contributed to the development of the course materials. (PDF)

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