Is the Configuration of Magnetic Fields Only a Convention?

[weirdoguy]

Well, if magnetic fields are defined by the force they apply to moving charges, then it follows that magnetic field would do work.

Then show us your calculations that prove that.

 

[cg0303]

I think the OP would like to drop the concept of the magnetic field, instead using some field they (confusingly) keep calling a magnetic field

My question is whether the magnetic field could have been defined differently. A differently defined magnetic field would still be called a magnetic field.

 

[Ibix]

My question is whether the magnetic field could have been defined differently. A differently defined magnetic field would still be called a magnetic field.

Maybe. It's still confusing to refer to your hypothetical definition by the same term used for a mainstream concept.

I notice you didn't comment on the rest of my post. Am I correct in understanding that you want to define a field that points in the direction $\vec v\times\vec B$?

By the way, if you are still able to edit your post would you mind removing the "of" you seem to have inserted after "instead" in your quote of my post?

 

[cg0303]

Then show us your calculations that prove that.

I made a mistake. I mistakenly thought that if the magnetic field and the force on the charge were not perpendicular, the magnetic field would do work. In reality, only if the charge's velocity and the force on the charge were not perpendicular, the magnetic field would do work.

An embarrassing mistake on my part. You were right in pushing me to show my calculations, that way I caught it.

 

[cg0303]

Maybe. It's still confusing to refer to your hypothetical definition by the same term used for a mainstream concept.

I notice you didn't comment on the rest of my post. Am I correct in understanding that you want to define a field that points in the direction $\vec v\times\vec B$?

By the way, if you are still able to edit your post would you mind removing the "of" you seem to have inserted after "instead" in your quote of my post?

I don't know what else to call it. I guess I could just say the "hypothetic magnetic field".

Yes, I want to define a field that points in the direction of v × B.

 

[cg0303]

By the way, if you are still able to edit your post would you mind removing the "of" you seem to have inserted after "instead" in your quote of my post?

Done

 

[weirdoguy]

Yes, I want to define a field that points in the direction of v × B.

But how would it work when there is no moving charge and hence no $\vec{v}$? How would you describe interaction of two magnets?

 

[Ibix]

Yes, I want to define a field that points in the direction of v × B.

In addition to @weirdoguy's point, then, how do you define this field when two or three particles pass through the same point with different velocities? Your field has different strengths and directions from the same source at the same point.

Done

Thank you.

 

[vanhees71]

I think the OP would like to drop the concept of the magnetic field, instead using some field they (confusingly) keep calling a magnetic field, which points in the direction $\vec v\times\vec B$ ("in the direction of the force on the test moving charge", as in #43). OP seems to feel that this would be more intuitive.

It seems to me that this implies that the force field isn't well defined, since two charges may pass through the same point with different velocities. Unless I, too, fail to understand what the OP wants.

Ok, but this doesn't make sense from a conceptual point of view. The important paradigm change from Newtonian mechanics, where interactions are treated as action-at-a-distance forces, is the concept of locality, i.e., one introduces fields as "mediators" of interactions. In Newtonian mechanics you can also take this standpoint of the field concept, but there it doesn't really change the qualitative picture, because all that's done is to introduce a static field. In practice that are electrostatic fields and the gravitational field. However, the idea is already clear in these cases: You first calculate a field, independent of the test particle moving "in this field", which mediates the interaction/forces.

E.g., in Newtonian theory of gravity you start with the field equation
$$-\Delta \Phi(\vec{x})=-4 \pi G \rho(\vec{x}),$$
where $\rho$ is the mass distribution of the "source of the gravitational field". The solution of course is
$$\Phi(\vec{x})=-G \int_{\mathbb{R}^3} \mathrm{d}^3x \frac{\rho(\vec{x}')}{|\vec{x}-\vec{x}'|}.$$
Then the gravitational force on a test mass is given by the potential
$$U(\vec{x})=m \Phi(\vec{x}).$$
the important point here is that the field $\Phi$ is independent of the test mass, upon which the force acts.

The same you have with electrostatic fields as well as magnetostatic fields and test charges in Newtonian physics. The important point also here is that the field is independent of the properties of the test charge. So no quantities related to it appear in the fields, neither the charge nor the charge's velocity.

The field concept and the locality concept becomes, however, crucial in the context of relativistic physics, where the fields necessarily becomes a dynamical entity of its own. It's not just a mathematical trick to "mediate forces" but is a fundamental dynamical "thing" for itself, as "point particles" or "fluids" are fundamental dynamical entities for themselves within classical physics. The strict locality in space and (!) time of the successful dynamical models within the theory of relativity are key for the consistency with relativistic spacetime models and particularly causality.

To make a long speach short: It doesn't make sense to intermingle properties of the (test) particles/fluids with the field but keep everything within a strictly local description.

 

[cg0303]

But how would it work when there is no moving charge and hence no $\vec{v}$? How would you describe interaction of two magnets?

Magnets have the properties they do because of the motion of the charges inside them. It would probably take a lot of work to figure out how to apply the hypothetical magnetic field concept to two magnets, but it seems possible in principle.

 

[cg0303]

In addition to @weirdoguy's point, then, how do you define this field when two or three particles pass through the same point with different velocities? Your field has different strengths and directions from the same source at the same point.

Thank you.

Good point, I didn't think of that.