Understanding the Relationship Between Moving Electrons and Magnetic Fields

[roger]

Hello

I just wanted to know why a moving electron causes a magnetic field to be generated ?

I would require a rigorous description...


thanx

Roger

 

[Rob Woodside]

When boosting to another inertial frame electric and magnetic fields do a little mixing, just as space and time do to keep the speed of light constant. Read some relativity!

 

[pervect]

There isn't any general answer for "why" questions, but it's useful to know that relativity would not stand without the magnetic field. In relativity, the electric and magnetic fields "mix together" much like time and space, becoming inseperable. What looks like an electric field to a stationary observer becomes a magnetic field to a moving observer, just as what "looks like" time to one observer "looks like space" to another. Thus a description of electromagnetism involving only electric fields would not be complete according to relativity theory. Mathematically, the unified electric and magnetic fields are described by the "Faraday Tensor" http://scienceworld.wolfram.com/physics/ElectromagneticFieldTensor.html

 

[roger]

I understand, but outside of relativity, consider a moving electron in a vacuum...

I just wanted to know what causes the magnetic field in the first place ?


thanx

roger

 

[Rob Woodside]

I understand, but outside of relativity, consider a moving electron in a vacuum...

I just wanted to know what causes the magnetic field in the first place ?


thanx

roger

What would you accept as the cause? Does the charge cause the electric field? If so, then relativity requires a moving charge to cause a magnetic field in addition to the electric field.

 

[roger]

What would you accept as the cause? Does the charge cause the electric field? If so, then relativity requires a moving charge to cause a magnetic field in addition to the electric field.

Yes, I accept that charge is the source of the electric field, but how/why does it generate the magnetic field ?


Roger

 

[Rob Woodside]

Yes, I accept that charge is the source of the electric field, but how/why does it generate the magnetic field ?


Roger

Lorentz boost a pure electric field, in the new frame you will find a magnetic field depending on the direction of the electric field and the boost direction. As someone already said you should not think of electric and magnetic fields as disjoint, independently existing, fields. They are COMPONENTS of the electromagnetic field. Just as you can mix x and y components of a vector, if you rotate about the z-axis, you can mix electric and magnetic fields when you boost to a new inertial frame.

 

[pervect]

I understand, but outside of relativity, consider a moving electron in a vacuum...

I just wanted to know what causes the magnetic field in the first place ?


thanx

roger

It sounds like you're asking why is relativity true?

Recap: Why is there a magnetic field
answer: because of relativity

Question: but why is there a magnetic field?
answer: because of relativity - wait, I already said that once. Well, then...

Like most of physics, we observe the universe and determine _how_ it works. "Why" it works that way is ultimately a philosophical question.

 

[novaa77]

Dear Roger,
To put it simply, no one really knows why a moving electron creats a magnetic field. As a matter of fact even the concept of "field" has not been explained.In the case of gravity Einstein rejected the idea of a gravational field and proposed the space-time warp.

 

[rbj]

To put it simply, no one really knows why a moving electron creats a magnetic field.

as a matter of fact, i don't think that is true at all. we know why, considering the consequences of relativity, this fictitious force called the magnetic force appears to some observer when electric charges are moving relative to that observer.

i think what roger is asking about is: how does the magnetic force come to be because charges are moving? that can be predicted from the electrostatic action with special relativity taken into account.

it is not rigorous or at least not general (because it is a specific case with two lines of charge, not just a single electron or a pair), but i tried to explain it here: https://www.physicsforums.com/showthread.php?p=1260570#post1260570

 

[jtbell]

Dear Roger,

roger, have a read through Griffiths' Electrodynamics textbook

Hey guys, Roger's last post in this thread was over two and a half years ago.

 

[rbj]

Hey guys, Roger's last post in this thread was over two and a half years ago.

ooops.

they should lock these threads when they are inactive for some specific period of time (like 6 months). i never look, but when they are recently posted to, they appear at the top of the list to me.

 

[tabchouri]

sorry to continue again,

as a matter of fact, i don't think that is true at all. we know why, considering the consequences of relativity, this fictitious force called the magnetic force appears to some observer when electric charges are moving relative to that observer.

i think what roger is asking about is: how does the magnetic force come to be because charges are moving? that can be predicted from the electrostatic action with special relativity taken into account.

it is not rigorous or at least not general (because it is a specific case with two lines of charge, not just a single electron or a pair), but i tried to explain it here: https://www.physicsforums.com/showthread.php?p=1260570#post1260570

I agree completely, a magnetic field can be considered as a sole and unique result of the movement of charges with the respect of the observer. It is just an artifact introduced by that movement, if you will excuse the term.
An artifact that make us see another force, which is ONLY the result of electric force with movement and relativity taken into account.

Dear Roger,
To put it simply, no one really knows why a moving electron creats a magnetic field. As a matter of fact even the concept of "field" has not been explained.In the case of gravity Einstein rejected the idea of a gravational field and proposed the space-time warp.

And no, we pretty know why a moving charge creates a magnetic field.
And yes, we know what fields are.
IMO, I would say that Einstein proposed the space-time warp, SR and GR to ensure one sole property : the constancy of the speed of light in vacuum no matter the circumstance. May be there is no proper "gravitational field of force" in physical terms, it might be just an artifact that we observe following space-time warps: Remember also that the gravitational force is the most weird among the others since it is always attractive, and we only have one type of charge which is mass having a positive sign (contrary to electric +-), if i might say.
For physics sake, don't simplify the motivations and scheme of thought of that guy, he had an IQ of 167

-----------------------------------------------------
Correct me if I am wrong.
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[novaa77]

And yes, we know what fields are

.

Well tell us what fields are then, specifically electric and magnetic fields

 

[tabchouri]

.

Well tell us what fields are then, specifically electric and magnetic fields

Mathematically speaking, in a reference frame, a field of force, and in general a vector field, is the (infinite) set of vectors calculated at each point of the space (excluding time).
The electric field is the set of Electric potential vector al each point of space.
The magnetic field is the set of Magetic vector al each point of space.
The gravitational field ... and so on

Further, if you connect the points of space where the quantity measured (magnitude of the vector) is constant, you will have equi-potential curves.
The field lines are perpondicular to those curves.
From another POV, the field lines are the (fictitious) lines along which the vectors are tangential to the lines.

-----------------------------------------------------
Correct me if I am wrong.
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[tabchouri]

Now let us just forget about gravity.
If you consider for a moment, that the only physically real interaction between charges is the electrostatic force, it is obvious when the charges are at rest.
Now just consider the electrical interaction between them when they move compare to the observer, and apply the Lorentz transforms on their movement and SOLE electrical interaction. you will find that the interaction is different from the elecrical one when they are at rest (explicity, the force that they exert on each other does not pass through their centers, AS when they are at rest). The extra (non axial) force, which we call Magnetic force, IS SOLELY and EXCLUSIVELY the result of the electrical interaction transformed through relativity (Lorentz) due to their movement.

-----------------------------------------------------
Correct me if I am wrong.
http://ghazi.bousselmi.googlepages.com/présentation2

 

[novaa77]

Mathematically speaking, in a reference frame, a field of force, and in general a vector field, is the (infinite) set of vectors calculated at each point of the space (excluding time).
The electric field is the set of Electric potential vector al each point of space.
The magnetic field is the set of Magetic vector al each point of space.
The gravitational field ... and so on

Lets say if some one were to ask what makes an airplane stay up in the air and if I was to reply that there is some guy upfront who is keep it up in the air, would I be wrong?

What you have stated above describes the nature of a field but does little to explain the mechanism behind it

 

[jtbell]

What you have stated above describes the nature of a field but does little to explain the mechanism behind it

That is correct. All of physics in fact, is fundamentally descriptive and predictive. It does not offer ultimate "explanations." Every theory has something at its root that is not "explainable" in the context of the theory, and must be taken as an assumption. Sometimes physicists come up with new theories which "explain" the assumptions of an earlier theory, but these new theories themselves always have assumptions.

 

[tabchouri]

That is correct. All of physics in fact, is fundamentally descriptive and predictive. It does not offer ultimate "explanations." Every theory has something at its root that is not "explainable" in the context of the theory, and must be taken as an assumption. Sometimes physicists come up with new theories which "explain" the assumptions of an earlier theory, but these new theories themselves always have assumptions.

I agree completely.

Now let us just forget about gravity.
If you consider for a moment, that the only physically real interaction between charges is the electrostatic force, it is obvious when the charges are at rest.
Now just consider the electrical interaction between them when they move compare to the observer, and apply the Lorentz transforms on their movement and SOLE electrical interaction. you will find that the interaction is different from the elecrical one when they are at rest (explicity, the force that they exert on each other does not pass through their centers, AS when they are at rest). The extra (non axial) force, which we call Magnetic force, IS SOLELY and EXCLUSIVELY the result of the electrical interaction transformed through relativity (Lorentz) due to their movement.

But what i tried to say is : the Magnetic field is a misleading one. It has no physical origin, unlike electric field. The magnetic field is a result of coordinates, velocities and acceleration (electostatic) transformations in the scope of Relativity.
Since I did not do it for several years, I'm not really acquinted with the math behind all those transformations. But it is important that you understand that magnetic field is just a side effect of the electric field, by means of mathematical transformations that bring the corrdinate system of the moving charges into the frame of the observer. I can't explain it further.
If you were to chose a suitable frame related to the charges, you will no longuer observe the distorsions of the electric interaction that you see in a resting frame : what we call the magnetic field.-----------------------------------------------------
Correct me if I am wrong.
http://ghazi.bousselmi.googlepages.com/présentation2