Why is magnetic field B along a straight wire circular not radial?

[warrenchu000]

Homework Statement

Why is B field circular?

Relevant Equations

Biot Savart Law; Lorentz contraction

Statement: The magnetic field around a straight wire carrying a current can be explained Relativistically by changing the inertial frame of reference to the frame of the moving electrons - i.e., a Lorentz contraction of the positive charges in the wire will give a denser concentration of the charges, therefore generating an electric field. The magnetic field seen in one frame now manifests itself as an electric field in another frame.

Question: What explains the circular direction of the magnetic field around the wire when the electric field points radially away from the wire? Why are the two fields perpendicular to each other when going from one frame to the other?

(Please don't cite any equations as the only reason. I am looking for a physical answer.)

 

[malawi_glenn]

Why are not equations physical reasons? The language of physics is math

 

[warrenchu000]

Why are not equations physical reasons? The language of physics is math

That's even more of an useless answer. You need to interpret the equations in a physical way.

 

[Orodruin]

Basically because the magnetic field is a pseudovector field and not a proper vector field:
https://www.physicsforums.com/insights/symmetry-arguments-and-the-infinite-wire-with-a-current/

 

[malawi_glenn]

That's even more of an useless answer. You need to interpret the equations in a physical way.

Radial B field would contradict Oerstedts experiment. Does not get any more physical than this. Not a single equation as a bonus.

 

[warrenchu000]

A negative argument does not shed any light why it is so - I know what Oerstedt's experiment shows.
The symmetry argument was not clear what was the point - that pseudovectors can be physically changed 90 degrees? That a charged particle can get pushed away in one frame while circling around a center in another frame?

 

[jbriggs444]

A negative argument does not shed any light why it is so - I know what Oerstedt's experiment shows.
The symmetry argument was not clear what was the point - that pseudovectors can be physically changed 90 degrees? That a charged particle can get pushed away in one frame while circling around a center in another frame?

Read Feynman on "why" questions. What things would you accept as premises for an answer?

 

[Orodruin]

A negative argument does not shed any light why it is so - I know what Oerstedt's experiment shows.
The symmetry argument was not clear what was the point - that pseudovectors can be physically changed 90 degrees? That a charged particle can get pushed away in one frame while circling around a center in another frame?

You are drawing erroneous conclusions. Mainly because you do not seem to understand the mathematics behind electromagnetism.

 

[robphy]

Radial B field would contradict Oerstedts experiment. Does not get any more physical than this. Not a single equation as a bonus.

An outward radial B field would violate Gauss’ Law for Magnetism.

 

[robphy]

The magnetic field as an arrow is peculiar to three dimensional space.
Arguably, it’s more fundamentally a bivector or 2-form, depending on one’s starting point.

The “pseudo-“ part of psuedovector is entwined with the “right hand rule” as a feature of the magnetic field.

The bottom line is that electric field and the magnetic field are different “physical” objects (as particular sets of components of a field tensor in spacetime) and thus have different mathematical representations, possibly blurred by additional structure that we have to recognize is there.

When I teach E&M to more advanced students, I emphasize that one never adds an electric field vector and a magnetic field vector… even if one has numerical constants that make the units compatible. It’s like somehow adding a vector and a plane. (Hold off on any reference to geometric algebra.)

Note that in the Lorentz force, only the magnetic force is associated with the velocity vector of the charge…. and requires the cross product with the magnetic field in order to get a [polar] vector, which a force is.

 

[warrenchu000]

Forget this forum. Just a lot of mumbo-jumbo answers. I don't need to defend myself about my background. I've gone through all the derivations in my old E&M textbooks (Corson & Lorrain, Jackson, Griffiths) but found no satisfactory answers. Yet.
Good bye.

 

[Orodruin]

don't need to defend myself about my background.

Considering that you clearly do not understand how electromagnetism works, it is not a matter of defending anything, it is a matter of learning how it works. That you do not understand how it works is evidenced, for example, by this statement:

That a charged particle can get pushed away in one frame while circling around a center in another frame?

It does circle in either frame. The magnetic force is not parallel to the magnetic field, it is orthogonal to it. You also say you do not want a mathematical argument, but that is not the way to understand things. The way to understand is to understand the mathematics. The mathematics is how theory is converted to predictions and those predictions are very well tested and confirmed to be a good description of nature. If your question is why a particular set of mathematics describes nature and not another, then you will always be disappointed because there can be no answer to that, see #7.

 

[robphy]

The magnetic field seen in one frame now manifests itself as an electric field in another frame.

Question: What explains the circular direction of the magnetic field around the wire when the electric field points radially away from the wire? Why are the two fields perpendicular to each other when going from one frame to the other?

(Please don't cite any equations as the only reason. I am looking for a physical answer.)

Forget this forum. Just a lot of mumbo-jumbo answers.

So, without "cit[ing] any equations", how do you justify "The magnetic field seen in one frame now manifests itself as an electric field in another frame"? (And can you make a more precise statement about the details?)

The transformation laws are rather complicated and I think it is a challenge for anyone
to describe the situation with any precision without equations.
(I don't think I've ever seen a convincing handwaving argument.)
Even with equations for the transformations of the field vectors,
I would argue that it's difficult to "read off the physics" in a way that would be satisfactory.
( Here are the equations for part of the transformation:
see "The Lorentz transformation of the Electric Field in 3-vector form" in
https://www.physicsforums.com/insig...rver-a-relativistic-calculation-with-tensors/ )

I would argue (as I did above) that part of the problem at hand is that
the traditional vector representation of the electric and magnetic fields (which are observer-dependent)
are not well-aligned enough with the spacetime viewpoint
to satisfactorily understand their relationships between inertial frames
(i.e. their transformations under a Lorentz transformation).

I claim that the vector representation obscures "the physics".
I argue that the "spacetime viewpoint" captures "the physics"
better than the frame-dependent vector representation found in textbooks.
But we need a better picture than "a vector field and pseudovector field, and their sources",
subject to Maxwell Equations.

That is to say, I think a better picture (a better representation) will allow
a more-convincing handwaving argument to be developed...
..akin to how spacetime diagrams allow more convincing explanations
of various non-intuitive "effects" of special relativity,
rather than sketching shrinking boxcars moving relative to each other.

By the way, I think you asked a very good question.
I think you have to be patient
and understand the limitations of the typical vector representation.

Until then, as @malawi_glenn says, we have to use math.

The language of physics is math

 

[warrenchu000]

I have resolved my issue: The force on a particle from a magnetic field is qv X B - in a direction perpendicular to both v and B. That direction is radially towards the wire, which can be explained as a current-induced magnetic field in the frame of the stationary charge or as a Lorentz-contraction excess-charge-density induced electric field in the frame of the moving current. In both inertial frames, the force is radially towards the wire.
My mistake was not remembering the B field force on a particle is perpendicular to the B field - as any freshman would know. Sorry!

 

[warrenchu000]

This also illustrates why a magnetic field does no work (the force and velocity are perpendicular; it can only deflect a particle). Work is a scalar quantity; it cannot be changed from a change in inertial frames, as can be with B.
******
If a theory is a house, the equations are the bricks.
Citing equations alone without using them to support the overall concept is like looking at a pile of bricks; it doesn't prove anything.
Also: Don't be afraid to admit your mistakes. You can learn a lot from them.