Quetion about direction of magnetic field lines

[mesa]

I see textbooks assign directions to magnetic field lines, for example north poles extending outward and south flowing inward. Are these directions correct or just a way to help tie the concept together and have just been arbitrarily picked much in the same way as conventional current?

 

[cepheid]

There is no distinction between the direction being "correct" and the direction being determined by the definition that applies to magnetic fields. "Correct" has no meaning beyond this. Every physical quantity has a definition that has been chosen in some way. So, I'm not sure what you are asking.

 

[mesa]

There is no distinction between the direction being "correct" and the direction being determined by the definition that applies to magnetic fields. "Correct" has no meaning beyond this. Every physical quantity has a definition that has been chosen in some way. So, I'm not sure what you are asking.

I am sorry I thought my question was clear, let us try again.

You brought up looking at my question through the definition of magnetic fields so we should start here. I understand fields to be a way to look at long range forces from interactions between B_f's. Magnetic fields can be represented as vector quantities at any point in space and as such I am asking about their direction. Text books show field lines for north poles directed outwards and south poles inward. My question simply is, are these vectors known to propagate in these directions or is it un-established and just arbitrarily assigned?

 

[Dadface]

Arbitary. I guess that at some time in the past somebody probably defined the direction of the magnetic field at a point as being the direction of the force acting on an isolated north pole if placed at that point.Or words to that effect.

 

[mesa]

Arbitary.

Very good, thank you.

 

[cepheid]

I am sorry I thought my question was clear, let us try again.

You brought up looking at my question through the definition of magnetic fields so we should start here. I understand fields to be a way to look at long range forces from interactions between B_f's. Magnetic fields can be represented as vector quantities at any point in space and as such I am asking about their direction. Text books show field lines for north poles directed outwards and south poles inward. My question simply is, are these vectors known to propagate in these directions or is it un-established and just arbitrarily assigned?

You might accuse me of being pedantic, but I still take issue with your wording here. Firstly, I don't know what you mean when you ask if the vectors "propagate" in these directions, esp. if we are taking about static electric and magnetic fields. Perhaps "point" would be a better word. My second issue is that your statement still seems to imply that there could be a discrepancy between the way these vectors "actually point" (red) and how we arbitrarily define them to point (blue). This is NOT the case. The first half of the sentence (red) is actually just totally meaningless without the second half (blue): they point in whatever direction they are defined to point, so it is not possible for these two things to be discrepant. It's NOT "unestablished." It's totally established, by definition.

Example: the direction of the electric field at a point in space is defined as the direction in which a positive test charge would accelerate if placed at that point in space. If you were to reverse that definition, and instead define it as the opposite of the direction that a positive charge would accelerate (or, equivalently, as the direction that a negative charge would accelerate), then the field vectors would, in fact all point in the opposite direction from what they did before. This change of definition, of course, has absolutely no effect on what is actually observed. Charges of a given polarity would still accelerate in the same directions as they did before. The effect of this quantity called the "E-field" would simply be defined to be the opposite of how we define it. Similarly, the direction of a magnetic field at a point in space has arbitrarily been defined to be the direction that a compass needle would point if placed at that point in space. However, we could easily have defined it in the opposite way if we had wanted.

 

[mesa]

You might accuse me of being pedantic, but I still take issue with your wording here.

If you call helping clear up the way I presented a question pedantic then please do so, it's the answer that matters and if I am not presenting correctly then that needs addressed first.

Firstly, I don't know what you mean when you ask if the vectors "propagate" in these directions, esp. if we are taking about static electric and magnetic fields. Perhaps "point" would be a better word.

In using the term 'propagate' I was applying it more directly to the fields with vectors more specifically directional at given points within these fields. I understand propagate typically refers to waves although even 'static' fields 'propagate' from the source whether charge or a dipole at 'c', if I am not using the proper term for this then present it.

My second issue is that your statement still seems to imply that there could be a discrepancy between the way these vectors "actually point" (red) and how we arbitrarily define them to point (blue). This is NOT the case. The first half of the sentence (red) is actually just totally meaningless without the second half (blue): they point in whatever direction they are defined to point, so it is not possible for these two things to be discrepant. It's NOT "unestablished." It's totally established, by definition.

Example: the direction of the electric field at a point in space is defined as the direction in which a positive test charge would accelerate if placed at that point in space. If you were to reverse that definition, and instead define it as the opposite of the direction that a positive charge would accelerate (or, equivalently, as the direction that a negative charge would accelerate), then the field vectors would, in fact all point in the opposite direction from what they did before. This change of definition, of course, has absolutely no effect on what is actually observed. Charges of a given polarity would still accelerate in the same directions as they did before. The effect of this quantity called the "E-field" would simply be defined to be the opposite of how we define it. Similarly, the direction of a magnetic field at a point in space has arbitrarily been defined to be the direction that a compass needle would point if placed at that point in space. However, we could easily have defined it in the opposite way if we had wanted.

Very good. By 'un-established' I only meant if vectors drawn in fields do have 'direction' we do not know which it is.