# Why does a changing electric field cause a magnetic field?

## Main Question or Discussion Point

I am three days away from my E&M finals exam and still I cannot understand this phenomena.
What I mean by that is that I can solve questions and apply the mathematical equations I just don't understand what is going on under the hood, what happens when an electric field changes and how does it translate into a change in the magnetic field?

Any help is appreciated,
nashed.

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One cannot answer 'why' questions in physics. At least, not usually to the asker's satisfaction. Is it enough to point to Maxwell's equations as a description of what is going on 'under the hood?'

Can you tell me why objects resist changes in motion? If you tell me anything other than something like 'that's the way nature appears to behave' then you have left the realm of physics and have entered the realm of metaphysics.

What I mean by why isn't "why does nature behave this way", I mean what is the underlying mechanisim?
For example, consider a conducting frame inside a magnetic field which is changing with time, this situation can be alternatively viewed as a magnetic field having fixed values in space and a frame that is moving inside the field, picturing it this way we can see that a force is acting on the electrons inside the frame causing a current which can be related electromotive force and thus to an electric field.
That was the intuitive way of explaning why a changing magnetic field cuases an electric field, my question is what is the explanation for it going the other way around.

What I mean by why isn't "why does nature behave this way", I mean what is the underlying mechanisim?
Nobody knows yet...

I view the questions 'why does nature behave this way?' and 'what is the underlying mechanism?' to be the same question so I'm sorry if I'm not much help here. In the example you gave about magnetic flux generating an electric current: I personally don't get any additional insight into the underlying mechanism behind the phenomena by changing reference frames.

What if I throw you this question: where did the magnetic field in your example come from?

Unfortunately, I believe that zoki85 summed up the answer to your question.

jtbell
Mentor
I mean what is the underlying mechanisim?
Electric and magnetic fields are two aspects of a single entity, the "electromagnetic field." The electromagnetic field is represented by a tensor whose components are the vector components of the electric and magnetic fields.

To make an analogy or metaphor, when a rod rotates end over end around an arbitrary axis, the spatial components of its length change in ways that are related by the rigidity of the rod. Likewise, the different components of the electromagnetic field tensor can't change independently. Changes in some components must be associated with changes in other components, in order to maintain something called "local U(1) gauge symmetry".

Andrew Mason
Homework Helper
Why does a changing electric field cause a magnetic field?
A changing electric field does not cause a magnetic field. Moving charges cause a magnetic field. The electric field of the moving charges is not changing.

The magnetic field is best explained as a relativistic effect of the moving charges.

AM

A changing electric field does not cause a magnetic field. Moving charges cause a magnetic field. The electric field of the moving charges is not changing.

The magnetic field is best explained as a relativistic effect of the moving charges.

AM
I am referring to the Amper-Maxwell equation from maxwell's equations which clearly states that a changing electric field causes a change in the magnetic field.

Anywho thanks for all the answers, I suppose I"ll accept it as an experimental fact for now, although I'd like to understand someday the process at the microscopic level.

Andrew Mason
Homework Helper
I am referring to the Amper-Maxwell equation from maxwell's equations which clearly states that a changing electric field causes a change in the magnetic field.
This is a different question than the one you posed.

If constant charge in motion creates a constant magnetic field then it should not be difficult to imagine that a non-constant charge in motion would create a non-constant magnetic field. Think of the magnetic field around the region between the plates in a capacitor on which the charge is constantly changing.

AM

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this is a perpetual answer, I believe it has to do with quantum mechanics but I honestly do not know, I just accept it as a fact.

Dale
Mentor
Anywho thanks for all the answers, I suppose I"ll accept it as an experimental fact for now, although I'd like to understand someday the process at the microscopic level.
In any scientific theory there are a set of facts which are accepted without explanation, these are often called postulates or axioms. They are accepted because they fit the experimental facts well, as you mentioned. In classical EM, Maxwell's equations are simply postulated, so there is no way to explain them within classical EM.

However, there are two possibilities for gaining deeper understanding.

One is by the fact that it is often possible to rearrange what you consider an axiom and what you consider a derived consequence. In classical EM, you can derive the relativistic Lorentz transform from Maxwell's equations. Alternatively, you can derive magnetism from electrostatics and the Lorentz transform.

The second way is by getting a deeper, more general, theory. Then the postulates of the original theory can be derived as a special case limit of the consequences of the more general theory. In this case Maxwell's equations can be derived as the classical limit of a QFT field with U(1) gauge symmetry.

I am three days away from my E&M finals exam and still I cannot understand this phenomena.
What I mean by that is that I can solve questions and apply the mathematical equations I just don't understand what is going on under the hood, what happens when an electric field changes and how does it translate into a change in the magnetic field?

Any help is appreciated,
nashed.
"Few topics in modern physics have caused as much confusion and misunderstanding as that of displacement current."
http://en.wikipedia.org/wiki/Displacement_current

So perhaps this was not an exam problem ;-)

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