Kirchhoff's Loop Rule Is For The Birds

Summary

En este captivante script de video, el profesor Walter Lewin imparte un curso de física sobre electricidad y magnetismo, destacando la importancia de entender correctamente la ley de Faraday. Critica que muchos libros de física高等院校 tienen explicaciones erróneas sobre este tema, ya que los profesores no comprenden adecuadamente la ley. Lewin utiliza un circuito simple con resistores y un electromagnete para ilustrar cómo la ley de Faraday entra en juego cuando hay un cambio en el flujo magnético, lo que lleva a una EMF no nula y a una corriente en el circuito. Destaca la contradicción con la regla de Kirchhoff del circuito cerrado y cómo esto es un tema no intuitivo que puede confundir. Al final, motiva a los estudiantes a que estudien seriamente para tener éxito en su comprensión de la materia.

Takeaways

• 🧲 La lección es impartida por Walter Lewin sobre física, específicamente sobre electricidad y magnetismo, a petición de Jason Hafner, el profesor de física del estudiante.
• 🔌 Se menciona que la mayoría de los libros de física de universidad tienen un error común en la interpretación de la ley de Faraday, según Lewin, debido a que los profesores no la entienden correctamente.
• 📚 Lewin recomienda ver su conferencia número 16 y leer sus notas de la misma para comprender mejor el tema tratado.
• 🌀 Se describe un experimento con un circuito simple que incluye dos resistores y un electromagnetismo perpendicular al pizarrón, para ilustrar cómo cambia la flujo magnético y su efecto en un circuito.
• 📐 La integral de la fuerza eléctrica (E) dot producto con el elemento de longitud (dl) alrededor de un circuito cerrado no es cero cuando hay un cambio en el flujo magnético, lo que entra en conflicto con la regla de Kirchhoff para circuitos cerrados.
• ⚡️ Se introduce el concepto de Fuerza Electromotriz (EMF), que es el resultado de un cambio en el flujo magnético y que induce un corriente en el circuito.
• 🔆 La diferencia de potencial entre dos puntos en un circuito puede variar dependiendo de la dirección de la corriente y la posición de los resistores, lo que muestra la no intuición de estos fenómenos.
• 🔵 Se discute cómo el valor y la polaridad de la diferencia de potencial pueden ser diferentes en dos mediciones realizadas en dos puntos del mismo circuito, debido a la dirección de la corriente y la configuración de los resistores.
• 🔍 Se hace hincapié en la importancia de entender la ley de Faraday y cómo la mayoría de los libros de texto la presentan de manera incorrecta o engañosa.
• 🔌 Se presenta un ejemplo de un circuito con un solenoide (autoinductor) ideal, un capacitor, una resistencia y una batería, para demostrar cómo la ley de Faraday se aplica en circuitos con componentes reactivos.
• 📚 Se sugiere que los estudiantes lean las notas de la conferencia número 20 para comprender mejor los conceptos discutidos en la lección.

Q & A

¿Quién es Walter Lewin y qué propósito tiene su clase en este script?

Walter Lewin es un profesor de física que imparte una clase con el objetivo de enseñar sobre la electricidad y el magnetismo, específicamente sobre un aspecto que considera que la mayoría de los libros de física universitaria entienden incorrectamente, a saber, la ley de Faraday.

¿Por qué dice Lewin que la mayoría de los libros de física tienen algo incorrecto sobre la ley de Faraday?

Lewin argumenta que la mayoría de los libros de física tienen algo incorrecto sobre la ley de Faraday porque los profesores de física no la entienden adecuadamente, lo que resulta en una interpretación errónea de cómo se aplica esta ley en ciertos escenarios.

¿Qué es lo que Lewin sugiere que los estudiantes hagan para comprender mejor la ley de Faraday?

Lewin sugiere que los estudiantes deberían ver su conferencia número 16 y leer sus notas de la misma, ya que allí cubre temas relacionados con la ley de Faraday de una manera que considera más clara y precisa.

¿Cuál es el ejemplo práctico que Lewin utiliza para demostrar un concepto de electricidad y magnetismo?

Lewin utiliza un circuito simple con dos resistores y un electromagnetismo perpendicular al pizarrón para ilustrar cómo la ley de Faraday se aplica cuando hay un cambio en el flujo magnético y cómo esto afecta la corriente y el potencial diferencial en el circuito.

¿Qué es el 'flujo magnético' y cómo se define en el script?

El 'flujo magnético' es una cantidad definida como el integral del producto punto entre el campo magnético B y un elemento de superficie ds sobre una superficie abierta. En el script, Lewin lo asocia con el cambio en el tiempo que afecta el circuito eléctrico.

¿Por qué Lewin insiste en que los puntos A1 y A2, así como D1 y D2, son eléctricamente idénticos?

Lewin insiste en que los puntos A1 y A2, y D1 y D2, son eléctricamente idénticos porque están conectados a un alambre que no tiene resistencia, lo que implica que no hay diferencia de potencial entre ellos y, por lo tanto, pueden ser considerados como un solo punto desde el punto de vista eléctrico.

¿Qué implica Lewin cuando dice que 'Kirchhoff's loop rule is for the birds' y por qué?

Lewin utiliza la expresión 'Kirchhoff's loop rule is for the birds' para criticar la aplicación indiscriminada de la regla de Kirchhoff en situaciones donde el flujo magnético cambia, ya que esta regla predice que la suma de las fuerzas electromotrices en un circuito cerrado debe ser cero, lo que no es cierto cuando hay un cambio de flujo magnético.

¿Cómo se relaciona el 'EMF' o 'Fuerza Electromotriz' con el cambio en el flujo magnético según Lewin?

Según Lewin, cuando hay un cambio en el flujo magnético, el integral del producto punto entre la electricidad E y el elemento de longitud dl alrededor del circuito no es cero, lo que indica la presencia de una 'Fuerza Electromotriz' (EMF) que induce una corriente en el circuito.

¿Qué muestra el experimento de Lewin con el voltímetro V1 y V2 y qué conclusión se puede sacar de ello?

El experimento de Lewin muestra que el voltímetro V1 y V2, aunque miden la diferencia de potencial entre los mismos puntos A y D, muestran valores y polaridades diferentes. Esto demuestra lo no intuitivo y contradictorio que puede ser la aplicación de principios de electricidad y magnetismo en certas situaciones.

¿Qué es un 'autoinductor' o 'solenoid' en el contexto de la clase de Lewin y cómo afecta la corriente cuando se activan?

Un 'autoinductor' o 'solenoid' es un dispositivo que consiste en un alambre enrollado en forma de espiral y que tiene la capacidad de almacenar energía magnética. En el contexto de la clase de Lewin, el autoinductor es idealizado como un conductor supercondutor, lo que significa que no tiene resistencia interna y, por lo tanto, no puede haber un campo eléctrico dentro de él cuando la corriente comienza a fluir.

¿Cómo Lewin describe el comportamiento de la corriente y el potencial diferencial en un circuito con autoinductor, resistencia, capacitor y fuente de voltaje?

Lewin describe que cuando se cierra un switch en un circuito de este tipo, la corriente comienza a fluir y, debido a la presencia del autoinductor, la corriente no es instantánea. El potencial diferencial a través del autoinductor no es cero y está relacionado con la tasa de cambio de la corriente con el tiempo, lo que se describe mediante la ecuación de Faraday y la ley de la autoinducción.

¿Por qué Lewin critica a los libros de física universitarios por 'hacer trampa' al escribir las ecuaciones de circuito?

Lewin critica a los libros de física porque, a pesar de obtener resultados correctos, utilizan una forma errónea de escribir las ecuaciones de circuito que no respeta la ley de Faraday. Según él, esta forma incorrecta de presentar la física puede llevar a malentendidos conceptuales y a una comprensión incorrecta de los estudiantes.

¿Qué consejo le da Lewin a los estudiantes de la clase de Jason y a aquellos que toman el curso edX de Electricidad y Magnetismo?

Lewin alienta a los estudiantes a tomar el curso seriamente, esforzándose en las tareas y los exámenes, y les asegura que, si lo hacen, tienen muy buenas posibilidades de pasar el curso. Les desea suerte en sus estudios.

Outlines

00:00

🧲 Introducción a la Ley de Faraday y su malentendido común

El profesor Walter Lewin presenta un experimento de física sobre la ley de Faraday, destacando que muchos libros de física高等院校理解错误。 Utiliza un circuito con dos resistores y un electromagnet para ilustrar cómo la ley de Faraday se aplica cuando el campo magnético cambia rápidamente y permanece constante. Expone que la integral de E dot dl alrededor del circuito no es cero cuando hay un cambio en la flujo magnético, lo que implica que la regla de Kirchhoff no se puede aplicar en esta situación.

05:06

🔍 Desafío a la Regla de Kirchhoff en contextos magnéticos

Lewin cuestiona la validez de la regla de Kirchhoff en presencia de un campo magnético cambiante, demostrando matemáticamente que la integral de E dot dl no es cero y presentando el concepto de fuerza electromotriz (EMF). Explica que la dirección de la corriente inducida dependerá de si el campo magnético está aumentando o disminuyendo, y cómo esto afecta la medición de potencial en diferentes puntos del circuito.

10:14

🔌 Diferencia en mediciones de potencial debido a la inducción

El profesor Lewin ilustra cómo la medición del potencial entre dos puntos del circuito puede dar resultados y polaridades diferentes dependiendo de la ubicación de los medidores de voltaje (V1 y V2). Utiliza un ejemplo con resistores R1 y R2 y una corriente inducida para demostrar cómo los medidores pueden mostrar lecturas dispares e incluso con polaridad invertida, subrayando la no intuición de estos fenómenos.

15:18

📚 Recomendación de recursos y discusión sobre la inducción

Lewin hace una pausa en la explicación para recomendar la asistencia a la conferencia 16 y la lectura de los apuntes correspondientes para comprender mejor la ley de Faraday. Discute brevemente cómo la dirección de la corriente inducida cambia con el aumento o disminución del campo magnético y prepara el escenario para el siguiente tema, un circuito con un solenoide ideal (autoinductor).

20:18

🌀 Explicación de un circuito con autoinductor y su comportamiento

Se presenta un circuito que incluye un autoinductor hecha de alambre superconductor, un resistor, una baterías, una capacitor y un interruptor. Al cerrar el circuito, se describe el flujo de corriente y cómo la ley de Faraday (integral de E dot dl) no es cero debido a la presencia de un autoinductor. Se resalta que la integral de E dot dl a través del autoinductor es nula porque no hay resistencia y, por lo tanto, ningún campo eléctrico dentro del mismo.

25:25

⚡ Crítica a la aplicación incorrecta de la ley de Kirchhoff en textos académicos

Lewin critica la forma en que muchos libros de física高等院校 aplican incorrectamente la ley de Kirchhoff al escribir la ecuación de un circuito con autoinductor, a pesar de que llegan al resultado correcto. Expone que la ecuación honesta, según la ley de Faraday, no debería ser nula y que la justificación de los autores de los libros es incorrecta y perjudicial para la enseñanza de la física.

30:33

🔧 Consideración de un voltímetro en el circuito y su medición

El profesor Lewin plantea un escenario hipotético donde se conecta un voltímetro al circuito y cuestiona qué medirá el voltímetro, desafiando la idea previa de que la integral de E dot dl a través de los alambres del autoinductor es cero. Sugiere que el voltímetro mostrará un valor de plus L dI dt, conectando esto con la autoinducción y dejando el tema para ser discutido por Jason en futuras lecciones.

35:38

🌐 Reflexión sobre la integración de E dot dl en diferentes caminos

Se describe un escenario donde se mide el campo eléctrico E tomando diferentes caminos alrededor del circuito, incluyendo un trayecto fuera del circuito y de regreso. Se resalta que, al elegir un camino que no tenga flujo magnético cambiante a través de la superficie, la regla de la integral de E dot dl de Kirchhoff se aplica correctamente, mostrando un valor de plus L dI dt.

🎓 Motivación y éxito en el estudio de Electricidad y Magnetismo

En el final del script, Lewin motiva a los estudiantes de la curso de Electricidad y Magnetismo impartido por Jason a que lo tomen en serio, haciendo homework y estudiando para los exámenes, para tener éxito en el curso. Agradece a aquellos que también han tomado su curso 8.01x y desea suerte a los estudiantes en sus esfuerzos educativos.

Keywords

💡Faraday's law

La ley de Faraday es un concepto fundamental en electromagnetismo que describe cómo un campo magnético cambiante induce una corriente eléctrica en un circuito cerrado. En el video, se utiliza para explicar cómo un cambio en el flujo magnético induce una fuerza electromotriz (EMF) y, por lo tanto, una corriente en el circuito, lo cual es central para entender la relación entre la electricidad y el magnetismo.

💡electromagnet

Un electromagneto es un dispositivo que genera un campo magnético utilizando una corriente eléctrica. En el script, el electromagneto es utilizado para crear un campo magnético que cambia con el tiempo, lo que induce una corriente en el circuito según la ley de Faraday, siendo esencial para demostrar los principios físicos discutidos.

💡magnetic flux

El flujo magnético es la cantidad total de campo magnético que atraviesa una superficie. En el video, el flujo magnético es crucial ya que su cambio en el tiempo es lo que induce una corriente eléctrica según la ley de Faraday. El script destaca la importancia de entender el flujo magnético para aplicar correctamente la ley de Faraday.

💡self-inductance

La autoinducción se refiere a la propiedad de un circuito, como un solenoide, de oponérse al cambio en la corriente eléctrica que fluye a través de él. En el script, el concepto de autoinducción es importante para entender cómo el cambio de corriente induce una EMF opuesta al cambio, lo que es un fenómeno clave en la electrónica y la física de los circuitos.

💡Kirchhoff's loop rule

La regla de Kirchhoff para los bucles, también conocida como la segunda ley de Kirchhoff, establece que la suma de las fuerzas electromotrices en cualquier bucle cerrado es igual a la suma de las caídas de tensión. En el video, se cuestiona la aplicabilidad de esta regla cuando hay un cambio en el flujo magnético, lo que lleva a conclusiones no intuitivas sobre la medición de la tensión.

💡electromotive force (EMF)

La fuerza electromotriz (EMF) es la energía por unidad de carga que es capaz de empujar la carga a través de un circuito. En el script, el EMF es inducido por un cambio en el flujo magnético y es esencial para entender cómo se genera la corriente en un circuito cerrado.

💡resistor

Un resistor es un componente pasivo en un circuito que oponiéndose a la corriente eléctrica. En el video, los resistores son utilizados para demostrar cómo la corriente y la tensión se ven afectadas por el cambio en el flujo magnético y son parte integral de los cálculos y demostraciones presentadas.

💡capacitor

Un capacitor es un dispositivo que almacena energía en el campo eléctrico. En el script, se menciona junto con otros componentes como parte del circuito que se utiliza para ilustrar cómo los campos eléctricos y magnéticos interactúan y afectan a la corriente y la tensión.

💡superconducting wire

Un cable superconductor es un material que, en estado de superconductividad, permite la transmisión de corriente eléctrica sin resistencia. En el video, se menciona que las conexiones entre componentes no tienen resistencia, lo que es una característica de un cable superconductor y es importante para las demostraciones físicas realizadas.

💡voltmeter

Un voltímetro es un instrumento utilizado para medir la diferencia de potencial eléctrico entre dos puntos. En el script, se discuten las lecturas de un voltímetro en el contexto de un circuito con cambios en el flujo magnético, lo que muestra cómo la tensión puede variar y tener polaridades opuestas dependiendo de la configuración del circuito.

Highlights

Walter Lewin teaches a lesson on electricity and magnetism, emphasizing the common misunderstanding of Faraday's law.

Lewin points out that most physics books incorrectly apply Kirchhoff's loop rule due to a misunderstanding of Faraday's law.

An improvised experiment is conducted using a simple circuit with two resistors and an electromagnet to demonstrate Faraday's law.

The concept of magnetic flux and its integral over an open surface is introduced to explain induced electromotive force (EMF).

Lewin explains that points A1 and A2, and D1 and D2, are electrically identical in the circuit, simplifying the analysis.

The contradiction between Faraday's law and Kirchhoff's loop rule when a magnetic flux changes is discussed.

Lewin demonstrates that the potential difference between points A and D can vary depending on the path taken in the circuit.

An example with specific resistances and induced current is used to illustrate the non-intuitive nature of the potential difference.

The experiment shows that the same points in a circuit can have different potential differences depending on the measurement path.

Lewin emphasizes the importance of understanding the changing magnetic flux and its effect on the induced EMF over time.

A solenoid or self-inductor made of super-conducting wire is introduced to explore the behavior of circuits with inductance.

Faraday's law is applied to a circuit with a self-inductor, showing that the closed loop integral of E dot dl is not zero.

Lewin criticizes college physics books for incorrectly using Kirchhoff's loop rule to explain circuits with self-inductance.

The concept of an ideal self-inductor with no internal resistance is used to derive the differential equation for an LRC circuit.

Lewin discusses the implications of measuring voltage across a self-inductor and how it relates to the rate of change of current.

The importance of taking the edX Electricity and Magnetism course seriously is highlighted, with a success rate of over 85% for serious students.

Lewin encourages students to read his lecture notes for a deeper understanding of the topics covered in the video.

Transcripts

I am Walter Lewin

and I'm going to teach you a little bit of physics

at the request of your own physics teacher, Jason Hafner.

We really don't have the right equipment for this,

so it's highly improvised.

But the goal is that I want to cover with you

something that is the most intuitive of all of electricity and magnetism.

So non-intuitive that almost all college physics books have it wrong.

Why do they have it wrong?

Because the physics teachers do not understand Faraday's law.

Yeah, you may be embarrassed to hear that, but it's true.

Almost all physics books have it wrong.

I will advise you to watch my lecture 16, I will--

Some of that I will cover now,

but you definitely have to read my lecture notes on lecture 16.

I have here a simple circuit with two resistors.

One resistor, which I call R2 and the other resistor I call R1.

All the wires here have no resistance, super-conducting wire.

And we have that at MIT.

You may not have that at Rice, but we have that at MIT.

Perpendicular to the blackboard, we have an electromagnet

and we can turn that electromagnet on.

That's all I am going to do

because the physics when turning it off is very similar,

so I will only discuss with you when we turn it on.

So the electric-- that magnetic field goes up very rapidly

and then stays constant.

And let's assume that that magnetic field is pointing out of the blackboard.

I could have chosen into the blackboard, but I'll take out of the blackboard.

As long as the magnetic flux--

and the magnetic flux is defined as the integral

of the magnetic field B dot ds over an open surface.

It's very important, an open surface.

And that open surface I will attach to this closed loop.

And you may choose that surface anywhere you want to,

but I want it to be attached to this closed loop.

I call this point here A1, this point here A2,

this one D2 and this one D1.

I want you to understand and appreciate that A1 and A2,

from an electrical point of view, are identical.

They are the same.

They are connected to a none-- to a wire that has no resistance.

So you can think of A1 and A2, if you want to, simply as A.

They are one and the same.

You'll see there's a reason why I split them.

And the same here-- D1 and D2 are also the same.

So you can think of this as one point A and one point D if you want that.

When the magnetic flux, the way I defined it,

is changing in time according to Faraday's law,

the closed loop integral around this circuit is not 0.

If the closed loop integral of E dot dl is not 0,

that means that Kirchhoff's loop rule does not work, cannot be used.

Using it is absurd.

Kirchhoff's loop rule would say that the closed loop integral of E dot dl--

the closed loop integral of E dot dl

will be 0 according to Kirchhoff.

I start here and I go all the way around,

and I come back here and that should be 0.

But that's not the case if there is a changing magnetic flux

the way I defined it.

The answer according to Faraday's law is that this is minus d phi--

the B makes use to [?] the magnetic field-- dt.

If the magnetic field is increasing,

because I turned it on all of a sudden, the magnet,

then clearly the magnetic field is not constant, magnetic flux is not constant.

So I'm going to get an integral E dot dl that is no longer 0.

We call that also often the EMF, Electromotive Force.

Therefore, there's a current going to run

and you can figure it out for yourself because I'm sure you'll cover it in class

that, in this case, where the magnetic field is increasing

and therefore, the flux is increasing,

that the current is in this direction, the current I.

And so this EMF, which is this integral, equals I times R1 plus R2.

So if we just look at our first eight minutes

and we notice that the red color that I'm using,

which worked so well at MIT in 26-100, resists camera, didn't come through so well.

And so whatever is red here, which was I, the current was this arrow.

I will put them in white.

I wish I didn't have to, but I will do that.

Otherwise, you may not see.

So the current is going around like this,

if that B field pointing out of the blackboard, is increasing.

Now, what now is the potential difference between A2 and D2,

between here and here?

Or I could say, what is the potential difference between A and D?

Because we agreed we can call this point A

and we can poll-- call this point D.

So the potential difference V A2 minus V D2

is the same as VA minus VD because A2 is A,

and D2 is D.

And that must be I times R2.

Very simple.

What now is the potential difference between A1 and D1,

which, of course, is also the potential difference between A and D?

So the potential difference between A1 and D1,

which is also VA minus VD--

now be careful.

The current is in this direction.

So this point has a lower potential than that point.

So it is not I times R1, but it is minus I times R1

because I go from here to there.

I will oppose the current.

Whereas here, I went with the current.

So it is minus I R1.

Now, it's staring you in the face now that Kirchhoff's loop rule is for the birds,

because if I measure here VA minus VD, then I get I times R2.

if I measure it here, which are at the same point,

I get minus I times R1.

They even have different polarities.

In other words, if I would put here a voltmeter V1,

that voltmeter would measure this value.

And if I put one on the other side, for which I have little room anymore,

that would measure this value.

And the voltmeter on this side I will call V

and I will call the voltmeter on this side V1.

And so what you see now is that V2 divided by V1 is minus R2 divided by R1.

Think about this for a minute.

Both voltmeters, this one and this imaginary one that I haven't drawn,

they both measure the potential difference between A and D.

Both voltmeters I will have plus up and minus down.

I will do the same here.

If the ratio of this resistance is 100,

then one voltmeter will read a value which is 100 times larger

than the other voltmeter.

But not only that, the polarity is reversed.

So this one might read plus 10 volts.

This one might read minus 1 volt.

So it's now staring you in the face how non-intuitive this is.

I can give you an example by making certain assumptions.

Suppose I have R1--

I think I chose 10 ohms and I have for R2 100 ohms.

And let us assume that at a particular moment in time,

this induced current-- it's induced by this changing magnetic flux,

that that induced current at that moment happens to be 10 milliamperes.

Keep in mind it will change with time.

Why will it change with time?

Because the EMF will change with time.

Why will the EMF change with time?

Because d phi dt will change with time.

I cannot keep the change of the magnetic flux constant all the time.

So let us assume that at a particular moment,

this induced I, which changes with time,

is 10 milliamperes.

Then you see that this voltmeter on the left side, V1,

will read 10 milliamperes times 10 ohms.

That is minus 0.1 volts.

Minus!

Keep that in mind.

It's minus.

This voltmeter, the plus is here, the minus is here,

will read a negative value.

A has a lower potential than D.

But V2 will read 100 times 10, 1 volt.

And I do this experiment in my lectures.

You will see it if you watch lecture 16 and you won't believe your eyes.

And I will show you, we'll have a small break now here for our eight minutes,

I will show you what actually you will see on an oscilloscope

when you put an oscilloscope here for V1

and at the same time, you demonstrate here the oscilloscope,

which shows you V2.

So we're going to put that on the board very shortly.

I want to repeat once more that the larger the value of d phi dt is,

the larger the EMF.

If the magnetic field is increasing,

then the current will be in a different direction,

the induced current,

than if the magnetic field is decreasing.

But those are details that Jason will discuss with you.

That's not really, at this moment, so important.

So let's now assume that the EMF is in this direction,

that the current is going around like this

and I'm going to make you now a sketch of what we will see.

Look what I did in the meantime.

I cleaned the blackboard and so now I have a nice opportunity

to add that voltmeter V2.

Here is the plus side of V2

and here is the minus side of that voltmeter.

So they are both hooked up in exactly the same way.

They both measure the potential difference between A and D

and they both get totally different values.

Let me make a drawing, a sketch of the magnetic field,

which is not the magnetic flux,

but simply in magnetic field that we produce in the lecture hall

as a function of time

when we turn on the electromagnet.

Um, I'll make some rough guess.

It starts with 0 and then this goes something like this.

And then if we keep the magnet on,

then, of course, the magnetic field will reach a maximum,

and we'll flatten off.

Notice that here, dB dt is 0,

so there's no longer any flux change.

But here, it's almost constant.

There is a flux change.

Let us first do V2 and this means plus.

So I would say between these two points, between here and here in time,

um, the flux derivative is roughly constant

because this-- this is almost a straight line.

And so it means that V2 will have a certain value.

In our case, with the example that we chose,

V2 was-- what was it? 1 volt?

Yes, I think so, plus 1 volt.

That's why I put that plus.

And when you are here, then d phi dt is 0,

so you must end up here again.

And I will just somehow sketch it that it gets down to 0.

So that's what you will see on the oscilloscope.

Then we show students, at exactly the same time,

we show them V1 as a function of time.

And since V1 is negative, I can use the same [INAUDIBLE], the same vertical.

Now, in our special example, V1 was 10 times smaller and negative.

Well, 10 times smaller is something like this.

So you'll get something like this.

And so the moment that we turn on the electromagnet,

we show the students, as a function of time,

millisecond resolution, V2 and V1

and these are the curves that you will see.

You see, in front of your eyes, the fact that one voltmeter, in this case,

reads a 10 times larger value than the other,

but also that the polarities are reversed.

When I did this experiment,

in my audience, was my good old friend,

very bright physics professor, Bob Ledoux.

This was a long time ago.

It was 1992, I think.

And Bob came to me after the lecture and he says, Walter, this cannot be.

There must be something wrong.

I said, Bob, I don't think so.

Give it some time.

I went to my office and the phone rang.

Who was on the phone? Bob Ledoux.

He says, Walter, I can't believe it.

It's true.

You see that even for physicists, this is not so obvious,

that the potential difference between two points,

measured one way and measured another way,

between exactly the same points,

totally different in value and different in polarity.

And so I really want you to watch this on lecture 16

and I want you to read my lecture notes on number 16.

If Kirchhoff's loop rule were to hold, which it doesn't,

then V1 and V2 should always measure exactly the same value.

I hope you realize that.

So you see, to use Kirchhoff's loop rule here, it's not even wrong, but it's criminal.

You get nonsense.

But Kirchhoff will predict that the potential difference between here and here

and here and here, is the same so that the closed loop integral of E dot dl,

that becomes 0.

All right.

You have something now to think about.

And now I will, again, stick with Faraday's law

but change the topic a little bit.

So maybe this is a good moment for Saif to have a break

and I will clean the blackboards.

I will show you a very simple circuit in which I put a solenoid,

a self-inductor as we call it.

It is an ideal self-inductor.

And what that means is that the self-inductor is made of super-conducting wire.

So the self-inductor has no resistance

and that means that there can never be an electric field

inside that self-inductor because the resistance is 0.

So keep that in mind, ideal self-inductor,

that the wires have no resistance.

There can never be an electric field in a self-inductor.

I have here a simple battery.

I chose just the simple battery model, that of an alternating current

because I'm sure that Jason will cover with you

these circuits with alternating current.

I just want to stick to the very basics.

So here is a battery and here is a resistance R.

Here is a capacitor C.

Here is a self-inductance L.

And then we close the loop.

And we have it here and in here, I'm going to put a switch.

So a self-inductor, which has no internal resistance.

The wire is a super-conductor, capacitor, resistance.

And let us assume for simplicity, although it's not important,

that the battery has no internal resistance itself,

or negligently small.

And let's assume that the value of the battery is V0.

So it remains constant.

I throw the switch.

Obviously, what's going to happen,

a current is going to flow in this direction

because this is the positive side.

So I wish I could do it with red, but that doesn't work so well on the camera,

so I will do it then with white.

So a current is going to run in this direction,

through a resistor in this direction,

in this direction through the self-inductance, in this direction,

in this directions and in this direction.

Now, what does Faraday say?

Faraday says that the closed loop integral of E dot dl,

it was minus d phi dt.

The magnetic flux is through an open surface, as I discussed earlier

and that open surface must be attached to your closed loop.

So the closed loop is this and so we must attach a surface.

Think of it as a soap film.

It doesn't have to be flat.

It could be curved.

It could be very strange in shape.

But it has to be an open surface that is attached to the closed loop.

And if you want to see how that looks inside the self-inductor,

it's very hard to see becomes almost like a staircase

that the soap will roam around

because it must be one open surface.

All right.

Now, we're going to write down the integral of E dot dl.

I really want to try this in a different color

and if it doesn't work, then Saif will tell me.

Do we agree that the E field here is in this direction?

Can you see it, or not so well?

The E field is in this direction in the resistor.

This side of the capacitor will become plus

because of the current flow

and so the E field here is also in this direction.

What is the E field in the wire of the self-inductor?

What do I hear?

What are you saying?

It's 0.

Exactly, because there is no resistance.

So E here is 0.

So the integral E dot dl through this wire is 0.

The E field here goes from plus to minus,

so the E field here is in that direction.

So now we are ready to write down the differential equation for this circuit.

And I will start at this point, I will go around

and I will come back at this point.

So the first value when I go in this direction is minus V0.

Right, I--

It is the integral of E dot dl, the angle between the two,

is 180 degrees,

so I get a minus sign.

In the resistor, it is plus I times R.

I changes in time, but at a particular moment in time it happens to be I.

Remember, the capacitor C equals Q divided by V.

I call this V of C.

And so we get plus Q divided by C.

That is E dot dl over the capacitor.

Yah, C is Q divided by V and so the potential difference,

which is, after all, the integral of E dl,

this VC is C divided by-- Q divided by C.

Now I come to the self-inductor and I'm crawling inside that wire.

And I go through that wire and I never see that E field.

I never see that E field.

In other words, the integral E dot dl between this point and this point is 0.

So I am back here now at this point where I started.

So according to Faraday's law, that is minus d phi dt,

for which Jason will tell you, that that is the same as minus L dI dt.

I will not explain why this takes this form.

I can't take that away from him.

He's dying to explain that to you.

So look at this equation now.

This is the closed loop integral of E dot dl.

That, according to Kirchhoff, would have to be 0, but it isn't.

It is minus L dI dt.

Now I'll tell you that almost all college physics books cheat.

They do it wrong, but they get the right answer.

Why would they get the right answer?

Because they know the answer.

They write the following.

They write in their book--

boy, [INAUDIBLE] this is-- they write minus V0 plus IR

plus Q divided by C plus L dI dt is 0.

So this is the honest way it should be written, according to Faraday's law

and this part is the closed loop integral of E dot dl.

The college physics books--

most of them are written by physics teachers

who do not understand physics-- they write it this way.

And then they say, do you know why this is 0?

Because of Kirchhoff.

They say, look, this is the closed loop integral of E dot dl

and that has to be 0 according to Kirchhoff.

This is not only wrong,

but as I said earlier, it is criminal.

Because this is not the closed loop integral of E dot dl.

This is the closed loop integral of E dot dl

and that is not 0.

So the simple fact that they put this term here

doesn't make the equation wrong,

but the physics stinks.

And this is very, very serious because if you start teaching students

a concept that is completely wrong, well, I have to calm down now.

But this is emotionally very important for me.

I would advise you to also read, definitely read,

my lecture notes number 20.

So I imagine by now you are awfully confused.

But at least you know, you've seen once, how to do things the correct way,

correct in terms of physics.

The fact that these two equations give the same answer,

well, of course, because the authors of the book know the answer.

I'm now going to cause you some sleepless nights.

And I'm going to attach here a voltmeter--

and now I'm going to ask you, "What will this voltmeter show?"

And you will probably say, "Well, didn't you say that the integral E dot dl

through the wires here is 0?"

So you would think that V here is 0.

But that's not true.

We know what that V is going to be.

It's going to be plus L dI dt.

In other words, this equation is now correct.

And you will say, no, what happened now with your d phi dt?

Well, what I have done in a clever way,

by going around the circuit

I have now no longer any changing magnetic fluxes

going through my open surface,

which is now attached to my new closed loop.

And my new closed loop, folllow me, is like this.

And look when I come here.

I bypass that self-inductance.

I go through the voltmeter and I'll come here and I'll come here.

And so now Kirchhoff's loop rule should hold,

and so the sum should be 0.

Therefore, it shouldn't surprise you that this plus L dI dt

is exactly what this voltmeter then will show.

I'm going to confuse you even more.

I'm going to remove this voltmeter--

and you hold in your hand an instrument

to measure the electric field E.

And you start here, you go around and you get this term,

you get this term, you get this term.

And now when you arrive here, you leave the circuit

and you go this way.

You can choose your path.

I don't care.

And you come back to the circuit here.

But while you are going this dotted line,

which could be just through the air like this,

you measure the integral of E dot dl over that path that you have chosen.

And what will that integral show?

Plus L dI dt.

Again, you have now chosen a-- a loop whereby there is no longer

any changing magnetic flux going through that surface,

and so Kirchhoff's loop woo-- loop rule works.

I would like Jason to discuss with you

why it is that that voltmeter would measure plus L dI dt

because clearly the L dI dt has to do with the self-inductance.

So I'll leave that up to Jason.

Got to leave something for him.

So before I go off the air,

I would like to say a few words to the many people

who are now taking this course, this edX course,

which is taught by Jason.

I would like, to many of you who may also have taken my 8.01x course,

almost everyone who took 8.01x seriously passed the course,

more than 85%, for those who took it seriously.

So my advice to you is, to all of you, maybe tens of thousands all over the world

who have been following this course, this edX course,

this Electricity and Magnetism course,

if you take it seriously, that means doing your homework seriously,

work hard on the exams,

you too are probably very likely going to pass.

I wish you good luck.