# Time varying magnetic field and faradays law of induction

According to faraday's law we say that , whenever a magnetic field varies with time it creates an "electric field" .

But I do not understand , how can a time varying magnetic field produce electric field. What's the mechanism behind it?? I have also read on internet that due to Lorentz transformation a magnetic field creates a an electric field but , why does a change in reference frame turn a magnetic field into an electric field And , also a time varying magnetic field creates an electric field in matter like conductors and also in empty space , how can there be an electric field in empty space where there are no charges I want to know the reason in terms of Relativity or quantum mechanics Thank you

• It is because space is not separate from time. They are linked. Everything that happens in space, happens in time too, and vice-versa. Electric and magnetic fields are spatial and temporal manifestations of the same thing - the electromagnetic field. – Andrei Geanta Sep 1 '18 at 8:10
• I am afraid this is a misconception. There is a big difference between a field and a wave. A field is called "static", but it also can move slower than light. A wave moves with the speed of light. A moving electric field (charges) can generate a static magnetic field (magnet). A moving magnetic field cannot generate a (static) electric field, but only a wave. In QFT, a wave is just photons flying away. They can interact with remote charges as if by applying electric and magnetic fields, but they are really a wave. So you are correct, a static electric field cannot be produces without charges. – safesphere Sep 1 '18 at 8:28
• It doesn't. Read my previous comment. A varying magnetic field generates an electromagnetic wave, not a field. A field and a wave are not the same thing. A wave consists of real photons, a field does not. Furthermore, you cannot have a varying magnetic field without charges. So the wave actually is created by the varying electric field of the moving charges while a magnetic field is always static (meaning slower than light). – safesphere Sep 1 '18 at 8:36
• The bottom line, the "mechanism" you are asking about, is that moving charges emit photons and these photons interact with remote charges. Mathematically you can see this as alternating electric and magnetic fields flying with the speed of light, but in reality it is photons. There are no fields without charges. Charges moving in space create a magnetic field. Charges moving in time create an electric field. So, depending on your speed relative to charges, the electric field becomes magnetic or magnetic becomes electric, but both are produced by moving charges. – safesphere Sep 1 '18 at 8:50
• It does not create a field, but it does create a wave, which is not static. Saying this differently, the current is created by electrons in the conductor absorbing incoming photons. The photons carry energy that converts to the electrical energy of moving electrons. Classical and quantum electromagnetism are not easily mixed together. While studying the classical theory you are better off by just taking it at the face value. So don't sweat it, just assume that what the book says is correct. You'll sort out these deep little details later after you become an expert in the Quantum Field Theory. – safesphere Sep 1 '18 at 8:58

I distinguish two good questions. Q1 is about Faraday's law and Q2 about field transformation. First Q2. E and B are components of an antisymmetric rank 2 field tensor. The values of E and B therefore depend on the reference frame. This is no different from velocity and energy, which as also depend on the reference frame . As to Q1, the rotation of B and the time derivative of E are two ways to write down the exact same thing, $$\partial_t \vec \nabla \times \vec A$$.
Change of reference frame turns magnetic field into electric field for the same reason, why change of reference frame turns the coordinate $x=0$ into $x\ne0$.