Kirchhoff's 2nd law wrongly used or not? Lewin vs all college books

In summary: I think my point was very clear. In the standard procedure for finding the force on a dielectric in a capacitor, you start off with the principle of virtual work. It says that the force on the dielectric is equal to the negative of the gradient of the potential energy of the system. And that is my point. You don't have to use the potential energy of the system. You can use any other energy function, and you'll still find the correct answer for the force. This is a problem because, for example, you could have easily used the total energy of the system. But the force you get from that is not the same as the force you get from using the potential energy of the system. This is a problem
  • #1
Feynmanfan
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MIT Professor vs. all college books

Hi there!

I'm a first year student and found quite interesting the MIT on-line video lectures on electromagnetism.
http://ocw.mit.edu/OcwWeb/Physics/8-02Electricity-and-MagnetismSpring2002/VideoLectures/index.htm [Broken]

In one these lectures given by Dr. Walter Lewin it is explained how all college books and teachers wrogly use Kirchhoff's 2md law in order to calculate the current through a RL circuit.

That is emf-IR-L (dI/dt)=0. Dr.Lewin says that this is the right answer but physically the procedure is not. In his lecture he states that Faraday's law is misinterpreted and not taken into account. He thinks that everybody knows that that's the differential equation, and just because they see a zero automatically we are using Kirchoff's law.

Lewin follows saying that Kirchoff tells us that the sum of V through a closed loop is 0, but how can it be zero if we have a change in magnetic flux. and therefore the closed integral of E.dl =-dflux/dt.

I couldn't convince my teacher. I am totally confused and don't know what to think.

What do you guys think? Is Lewin right? How can I convince my teacher?

Yours,

Santiago

P.S.: here's the lecture in PDF
http://ocw.mit.edu/OcwWeb/Physics/8-02Electricity-and-MagnetismSpring2002/LectureNotes/index.htm [Broken]
 
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  • #2
go Lewin

Lewin is correct.
E.dl =-dflux/dt is the correct law, but when using it in a circuit -dflux/dt is usually -L(di/dt) which is the potential over that component. However the flux part isn't really part of the closed circuit. Think of a closed circuit with no components, when the current changes there's a change in the flux and faradays law must be used, that is there's a contribution from L(di/dt) even thought its not seen in the circuit.

I don't think Lewin agrees that kirchhoff should get so much credit for using faradays law.
 
  • #3
Whatever Lewin says I would go with. I managed to get an A in my E&m class even while missing half my professors lectures by watching him online and paying close attention. I wouldn't recommend anyone do the same, but if you're going to be a slacker anyway, just do it! :wink:
 
  • #4
Feynmanfan said:
In one these lectures given by Dr. Walter Lewin it is explained how all college books and teachers wrogly use Kirchhoff's 2md law in order to calculate the current through a RL circuit.

That is emf-IR-L (dI/dt)=0. Dr.Lewin says that this is the right answer but physically the procedure is not. In his lecture he states that Faraday's law is misinterpreted and not taken into account. He thinks that everybody knows that that's the differential equation, and just because they see a zero automatically we are using Kirchoff's law.

You will notice as you proceed in your education that there are a lot more of these things going on - where the procedure gives you a correct (or at least an accurate enough) answer, but if you look "under the covers", there conceptual problems with it. A case in point is the force on a dielectric slab in an electric field.

Let's say you have a parallel plate capacitor maintained at a constant potential. You have a dielectric slab that is being pushed into the capacitor, where the front end of the slab is already in the capacitor while part of the rear of it still sticks out. The typical standard textbook procedure of finding the force on the slab starts off by using the principle of virtual work via

[tex]\vec{F}(\vec{r}) =- \nabla U(\vec{r})[/tex]

If you write down properly the electrostatic energy of the system using the assumption that the separation of the plates are very small when compared to the rest of its dimension, then you'll end up at the end with a force on the slab having only a component perpendicular to the parallel plates of the capacitor.

Already, there is a conceptual problem here. The E-field of the parallel capacitor is uniform going from one plate to the other. Yet, the NET FORCE on the dielectric is PERPENDICULAR to this field! The standard procedure in finding the force in this case produces the correct answer. But a student who is thinking about this long enough will notice a problem.

If one wishes to see what is the "under the cover" explanation of this, which is ignored in practically every E&M text, I highly suggest reading Ref. [1] below.

Zz.

[1] S. Margulies, Am. J. Phys. v.52, p.515 (1984).
 
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  • #5
I don't quite follow. The U in gradU to get the force is not the electrostatic potential. It is the electrostatic energry. Isn't it. I dons see why it's the wrong procedure.
 
  • #6
Taking the gradient of a scalar field gives you a vector field. Electrostatic energy is not a vector field.
 
  • #7
Taking the negative of the gradient of the electrostatic energy in a capacitor gets you the force on a dielectric put in it.THe energy is not the same inside the dielectric the outside. Right? In my contribution I didn't say electrostatic energy was a vector field. Obviosly, energy is a scalar
 
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1. What is Kirchhoff's 2nd law and how is it used?

Kirchhoff's 2nd law, also known as Kirchhoff's current law, states that the algebraic sum of currents entering and exiting a node (or junction) in a circuit must equal zero. This law is used to determine the current flowing through different branches of a circuit and to solve for unknown currents.

2. How is Kirchhoff's 2nd law commonly misused?

Kirchhoff's 2nd law is often misused by assuming that the current entering a node is equal to the current exiting the node, without taking into account the direction of the currents. This can lead to incorrect calculations and misunderstandings of circuit behavior.

3. What is the difference between Lewin's use of Kirchhoff's 2nd law and that of other college textbooks?

Walter Lewin, a renowned physicist and educator, uses Kirchhoff's 2nd law in a more intuitive and visual way compared to traditional textbooks. He emphasizes the concept of conservation of charge and uses diagrams and real-life examples to explain the law.

4. Can Kirchhoff's 2nd law be applied to all types of circuits?

Yes, Kirchhoff's 2nd law can be applied to all types of circuits, including series and parallel circuits. It is a fundamental law in circuit analysis and is used to solve complex circuits with multiple branches and nodes.

5. How can one avoid misusing Kirchhoff's 2nd law?

To avoid misusing Kirchhoff's 2nd law, it is important to pay attention to the direction of currents when applying the law. It is also helpful to use diagrams and visual aids to better understand the concept and correctly apply it to different circuits.

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