Exploring the Origin of Electric Field in F-N-L's Law

[Ryuzaky]

Good evening. Can anyone explain me the origin of the electric field in the F-N-L's law ?
I'm referring to this one :

[itex]\int_l \vec E^* d\vec l =-\int_s \frac{\partial \vec B}{\partial t} d\vec S[/itex]

where [itex]\vec E^*[/itex] is defined as (i'm reporting the words of the book) :
[itex]\vec E - \vec v \times \vec B[/itex].

in particular what is [itex]\vec E[/itex] and what is its origin.

//I apologize for any syntax/grammar error, I have to improve my English, I'm Italian.

 

[hexatrien]

It's the intensity of the electric field.


[itex]E[/itex][itex]=[/itex][itex]\frac{F}{q}[/itex],
where F is the force, which the field acts on the electric charge


Intensity of the electric field is used to characterize the electric field.

 

[Ryuzaky]

But that is the electrostatic field and its circuitation is 0 !

 

[cragar]

do you want to know where the E field comes from in faradays law or how E is related to B in that equation.

 

[sardar]

Hello,

Thank you for your question. The electric field in the F-N-L's law refers to the induced electric field that is created when a magnetic field changes over time. This is known as Faraday's law of induction, which states that a changing magnetic field will induce an electric field.

The origin of the electric field in this law can be explained by Maxwell's equations, specifically the Maxwell-Faraday equation. This equation states that the curl of the electric field is equal to the negative rate of change of the magnetic field over time. In other words, the electric field is created due to the change in the magnetic field.

To understand this concept better, let's break down the equation you mentioned. The first part, \int_l \vec E^* d\vec l, represents the line integral of the induced electric field along a closed path. This means that the electric field is being measured around a closed loop.

The second part, -\int_s \frac{\partial \vec B}{\partial t} d\vec S, represents the surface integral of the change in the magnetic field over time. This means that the rate of change of the magnetic field is being measured over a surface.

Now, to answer your question about the origin of \vec E, it is a combination of two factors - the electric field itself (\vec E) and the motion of the charged particles in the presence of a magnetic field (\vec v \times \vec B). This is known as the Lorentz force, which describes the force experienced by a charged particle in an electric and magnetic field. Therefore, \vec E^* represents the induced electric field due to the motion of charged particles in the presence of a changing magnetic field.

I hope this explanation helps to clarify the origin of the electric field in the F-N-L's law. If you have any further questions, please don't hesitate to ask.

Best,