Recent content by cg0303

Good point, I didn't think of that.

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.

Done

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.

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...

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

Well, if magnetic fields are defined by the force they apply to moving charges, then it follows that magnetic field would do work. It could be that in the end the physics still remains the same, but I'm not sure. I'm aware, as pointed out in #41, that this make take the thread outside the...

It would point in the direction of the force on the test moving charge. Although it would also be a matter of convention in the same way that electric field lines point away from positive charges by convention.

An argument can be made that while there is additional mathematical complexity, the fundamental idea behind it is simpler. This is because it makes magnetism more symmetrical with electricity because the magnetic field would diverge in the same way the electric field would (see post #4). The...

Sorry, you're right, it was Vanadium50. The reasons motivating it are in the OP.

In post #6 you described the field I was trying to describe in the OP as: "it would be some field like B×A so that it was perpendicular to both". So the other side of the equation would be B×A (if I understand correctly). Thank you!

Would you be able to show me how you derived this?

Just to clarify, the suggestion in the OP was not that we could eliminate fields in favour of forces acting-at-a-distance. Rather, it was that the definition of the magnetic field could be based on the force betwen currents, much like the definition of the elctric field is based on the forces...

Not at all! All I was trying to say is: a) There seems to be a historical motivation for the suggestion in the OP b) I don't see how Amperian forces between currents/moving charges could account for the circular path. Maybe I worded post #26 too strongly (although I kept saying 'I think' and...

1. It might only be complex with respect to its definition with respect to the vector potential. However, if we were starting from scratch (not that we would want to) and are defining B for the first time, it may not be as complex. I'm not using the words 'might' amd 'may' because I really don't...