Maxwell Equations without Faraday's Law

[kiki_danc]

Maxwell equations are composed of:

Gauss's Law
Gauss's Law for Magnetism
Faraday's Law
Ampere's law with Maxwell addition

If you take out Faraday's Law.. can other laws re constitute it? Or are they independent?

I want to know how the world would behave if there were no Faraday's Law. Note Faraday's Law is mostly related to generators, transformers, motors. So if this law didn't exist. Light would still behave the same and others?

 

[Dale]

If you take out Faraday's Law.. can other laws re constitute it? Or are they independent?

They are independent. If you remove Faraday’s law you cannot reconstitute it.

Light would still behave the same and others?

No, light would not work either. There would not be a wave solution of Maxwell’s equations

 

[kiki_danc]

They are independent. If you remove Faraday’s law you cannot reconstitute it.

No, light would not work either. There would not be a wave solution of Maxwell’s equations

Can one say motors and light differ due to the frequency of the magnetic and electric field?

So perhaps if only high frequency magnetic and electric field could be made to exist (for sake of discussion).. then only light can exist and all motors, generators would cease to function?

 

[Dale]

Can one say motors and light differ due to the frequency of the magnetic and electric field?

I would say that the more important difference is that light is a vacuum solution and motors are not vacuum. You can have “light” at arbitrarily low frequencies.

 

[kiki_danc]

I would say that the more important difference is that light is a vacuum solution and motors are not vacuum. You can have “light” at arbitrarily low frequencies.

What kind of light is produced at arbitrarily low frequencies? examples?

 

[fresh_42]

What kind of light is produced at arbitrarily low frequencies? examples?

https://en.wikipedia.org/wiki/Extremely_low_frequency

 

[kiki_danc]

https://en.wikipedia.org/wiki/Extremely_low_frequency

In unified theories or quantum electrodynamics.. is it possible to decouple high frequency em (light) from low frequency em (motors) by breaking or unbreaking symmetries? Meaning you let only high frequency em work and suppress all low frequency em from the laws of nature such that in another multiverse, motors can't exist but light can.. Or they are still binded together in even in any final theory?

 

[Dale]

Or they are still binded together in even in any final theory?

They become more closely bound in more advanced theories, not less. In most of them you cannot even write Faraday’s law separately.

 

[kiki_danc]

They become more closely bound in more advanced theories, not less. In most of them you cannot even write Faraday’s law separately.

Why, in our current incomplete theories.. can you write Faraday's law separately? How?

 

[Dale]

I don’t understand that question

 

[kiki_danc]

I don’t understand that question

You stated that "In most of them you cannot even write Faraday’s law separately.". So there is possibility that in our current theory we can write Faraday's law separately? how?

 

[Dale]

So there is possibility that in our current theory we can write Faraday's law separately? how?

Not just a possibility, a certainty:
$\nabla \times E = -\frac{\partial}{\partial t} B$

 

[kiki_danc]

Not just a possibility, a certainty:
$\nabla \times E = -\frac{\partial}{\partial t} B$

Any illustration or youtube video what they mean and how to write Faraday's law separately? How come in advanced theories... they become more closely bound?

 

[Dale]

Any illustration or youtube video what they mean and how to write Faraday's law separately?

I just showed you how in post 12.

How come in advanced theories... they become more closely bound?

Why did you randomly insert “...” in your question? It is very distracting and makes no sense. It looks like you are trying to add a pause, but it makes no sense to pause there.

They are more closely bound in the advanced theories because the advanced theories tend to use mathematical constructs where Faraday’s law is either a mathematical identity or it is combined with Gauss’ law for magnetism into a single equation.