Understanding the Flux Rule for Motional EMF?

[aaaa202]

The flux rule for motional emf can be stated as:

d[itex]\phi[/itex]/dt = -[itex]\epsilon[/itex]

I have some questions regarding this. 1) Should I find this rule intuitive?
And secondly a proof of this rule is given in my book, which I have attached. I don't really understand the idea of the proof - is the idea to proof the above rule or to just proof that if it works, it will do so for loops, which "do not even maintain a fixed shape". Because the words seem to suggest the later but on the other hand that would mean that the above rule is generally unproved in my book.

 

[harrylin]

The flux rule for motional emf can be stated as:

d[itex]\phi[/itex]/dt = -[itex]\epsilon[/itex]

I have some questions regarding this. 1) Should I find this rule intuitive?[..]

Just answering 1: You may find it intuitive by means of Lenz's law, which is a qualitative version of the above. It has similarity to Newton's third law, in the sense of action is reaction.

 

[aaaa202]

okay but Lenz' law is just a more qualitative statement of the flux rule - but perhaps there isn't more to it.
What about 2)? That one was more of a puzzle to me.

 

[harrylin]

okay but Lenz' law is just a more qualitative statement of the flux rule - but perhaps there isn't more to it.
What about 2)? That one was more of a puzzle to me.

It seems to prove the flux rule from their definition of flux plus the Lorentz force law. Both should appear earlier in the text.

 

[sardar]

I can provide some clarification on the flux rule for motional emf. This rule is a fundamental concept in electromagnetism and is used to describe the relationship between the changing magnetic flux and the induced emf in a conductor. It is based on Faraday's law of induction, which states that a changing magnetic field will induce an electric field in a conductor.

In the case of motional emf, this change in magnetic flux is caused by the motion of the conductor through the magnetic field. The flux rule for motional emf states that the rate of change of magnetic flux through a conductor is equal to the induced emf, with a negative sign. This means that the direction of the induced emf will be opposite to the change in magnetic flux.

To answer your first question, whether this rule is intuitive or not may vary from person to person. Some may find it intuitive based on their understanding of Faraday's law and the relationship between magnetic fields and electric fields. Others may find it less intuitive and require further explanation or examples to fully understand it.

As for the proof of this rule, the goal is to show that it holds true for any closed loop of any shape. This is important because it demonstrates the general applicability of the flux rule for motional emf, regardless of the shape or size of the loop. The proof shows that the induced emf is directly proportional to the rate of change of magnetic flux through the loop, and the negative sign ensures that the direction of the induced emf follows the right-hand rule.

In summary, the flux rule for motional emf is a fundamental concept in electromagnetism and is based on Faraday's law of induction. It may require further explanation and examples for some individuals to fully understand, but the proof demonstrates its general applicability for any closed loop. I hope this clarifies any confusion you may have regarding the flux rule for motional emf.