As we know through experiment, the magnetic force around a current carrying wire always points in the same direction given the direction of current, and this direction is described with the ‘right hand rule.’ What is it about the universe that has this ‘preference’ for this, and only this, direction?
Or from a mathematics perspective, why are our electromagnetic vector coordinates the way they are, and not the other way around? It seems the direction of fields is axiomatic to the equations, and something we tack on at the end after calculating magnitudes. For instance, “we just used ampere’s law to calculate the force at this distance from the wire, now to know the direction, let’s use the right hand rule.” Nowhere in the math does it say that the direction is a necessity.
It seems to just be an observed fact, and we have to include this fact in our equations. But this fact is not derived from the equations. For context, I understand that the electromagnetic equations can be solved with either a right or left convention. My question does not pertain to this convention, but the underlying nature of the universe and its ‘preference’ to follow the same direction every time given a direction of current. If it’s said the angular momentum of the vector causes this direction, then still it remains why this direction and not the other?
It all seems so asymmetric and arbitrary.
In: Physics
The direction of the force arrow as well as “direction” of current, and other things like “why this thing has negative charge” is just a mathematic convention. At some point some guy decided that this is it, and we just rolled with it because it’s fine either way.
The “direction of current” is not even the direction of the electrons inside the wire!
If I’m understanding your question correctly, you’re asking why the magnetic field field around a current always points the same way for a given direction of current, right?
First off, there is a sign convention in Maxwell’s equations, notably in Faraday’s law. In layman’s term (or ELI5 terms), it states that the voltage in a loop of wire is equal to the **negative** rate of change of the magnetic field going through that loop. Why negative? Because the loop is resisting the change of magnetic field going through it. This is why if you drop a magnetic down a copper pipe, it will slow down and fall much slower than the rate of gravity.
And the direction of the current that produces this opposing or negating magnetic field is dependent on both the pole of the magnet going through it, and the direction its moving. If you move a bar magnet back and forth through a loop of wire, and measure the current going through it, you’ll see the current change from + to – depending on which direction the magnet is moving. But either way, the current direction is always so that its resulting magnetic field **opposes** the rate of change of the magnetic field through the wire.
One explanation of magnetic fields around a conductor is that they are actually electric fields that appear because of relativistic length-contraction when charges are moving.
Because your motion relative to the moving negatively charged electrons in the conductor is different to the stationary positively charged atomic nuclei. Thus you will perceive length contraction on the electrons to be different than the atomic nuclei, either compressing or expanding the distance between the electrons, changing the apparent charge density of the electrons and the nuclei, and thereby creating an electrical field.
The right-hand rule and all that are consequences of the direction of motion etc.
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I probably explained that terribly. [Here’s a video that does a better job](https://www.youtube.com/watch?v=1TKSfAkWWN0).
When we discovered magnetic fields, we decided that magnetic field lines point north to south. It was an arbitrary decision, but we made it.
We also arbitrarily decided that current was the flow of positive charges. We then discovered the electron and realized it came from the negative terminal, so by the rules we had defined, it must have a negative charge.
The electric and magnetic fields always interacted in the same way even before we defined it. Even if you say magnetic field lines run from south to north, you just but a negative sign on all of our math and it works out the same. We just picked one way to stick with so everyone is on the same system.
It’s not a matter of sign convention. The right hand rule works the same if you swap conventional positive current with electron flow, and swap the force sensing particles charge from positive to negative.
What OP is asking is why the system behaves in the way we observe. For example, if you take two parallel wires with currents of the same sign traveling through them in the same direction, the magnetic force will cause the wires to be attracted to each other. If the currents are traveling in opposite directions then the wires will be repelled from each other. Why doesn’t the reverse occur?
IIRC the answer has something to do with relativity and how with electrostatic forces opposite charges attract.
Edit: This veritasium video https://youtu.be/1TKSfAkWWN0?si=IqvPYGrPhgzzz_lA
As I take it from your explanations, you want to know why electromagnetism cannot randomly “change direction”. So not any sign choices, but why the resulting directions are always the same, not sometimes opposite.
This for example follows if one accepts that physics is _continuous_, stuff does not jump. That alone does not yet fully prove that magnetic fields cannot randomly “flip”, but it would require them to weaken down to 0 first. To actually get the compatibility and non-zero-ness, you can take a second electric/magnetic device and compare.
So why continuity? Well, at some point we reach an area where “why” is not a reasonable question anymore. Simply because the inherent nature of physics prevents us from ever knowing the root cause; if such a thing even exists. Even if we somehow guess rules that exactly predict everything, then the underlying mechanism might still be different. Our observations just match the physics we currently use, so it is “good enough”.
Depending on what kinds of guesses you accept this kind of question is either physics (when we at least _could_ check it with enough effort), metaphysics (when we cannot but try to find the simplest mechanism that could underlay it), or religion (when we just believe).
This is actually due to bosonic fields having a polarity which goes towards the high which the high is the right hand spin by nature but technically just is a forward motion. An induced high potential induces forward motion in an inductor coil and levitation with a motion orienting the pin towards the center of the inductor (servo) which the direction of this spin is in the inertia vector of the levitated metal which tends to go in the direction of the first turn for a large crude inductor coil or for a small servo coil has no orientation or an orientation of a compass. This is because the voltage is variable across the inductor coil and this causes a torque from low weld point of high voltage to high weld point of low voltage of a torque starting from the coil start portion and ending at the coil end portion for a high voltage conductor. To answer your question for general servo this is because of the magnetic field of the earth primarially points towards the right hand except at the poles which there would be less servo levitation oscillation at the poles. This is related to toilets which toilets in the southern hemisphere flush oppositive and i am not sure but perhaps also this magnetic field difference exists in planets with two poles not the earth which then there is a right and a left hand spin as the earth’s magnetic field is always pointed upwards at the ionosphere.
I will paraphrase a joke that I heard: “Excellent question! Next question, please”.
“Why?” is the reason that we have scientists, explorers and philosophers. Surely there must be a reason, something that explains life and all that we can observe. And, over generations, we have observed and recorded certain behaviors. And for each observation, if we have enough evidence, we can formulate a rule or formula. And someone will invariably ask, “I’m not asking WHAT, I’m asking WHY. Can’t you give me a simple explanation?”
Well . . . no. For physical and biological sciences, the deeper we explore the more complicated it gets. (But why?)
At the smallest and the largest ends of the scales, the answers sometimes make little sense, but the math seems right. Quantum hoodoo. There are larger and smaller and yet unknown factors. (But why?)
Penultimately, if you ask someone to “explain it like I’m five”, depending on the question, the best answer is “because it is”. (But why?)
And ultimately, for five year olds, we answer, “Because I said so, now go to bed!” (But why?)
Not to mock you for your very good question, of course. The answer seems to be, “We know the WHAT pretty well, and it’s complicated, but we’re still working on the WHY. Check back every decade or so.”
I’m not a physicist, so the WHY question that you asked may actually have an answer. I’m pretty confident that the simplest explanation isn’t a kindergarten level, but a grad level thesis.
It may be simpler to ask “Why is there life?”
Imma say, “Good question, I’ll ask your mother. Now go to bed!”
Basically mathematical definition, thsts how the underlying math works we use to describe those phenomena.
All the tweak to match reality to math is done one or two levels below
It’s just a convention. When you go between any two actual measurable quantities, you apply the right hand rule an even number of times, so they cancel out and the convention itself is totally arbitrary.
For example, you can’t measure the “direction” of a magnetic field, you can just see the lines, but there’s no inherent arrow saying that they go in one direction or the other, we just chose to call one end north and the other south, and say that the lines point at the south pole.
If we used the left hand rule instead, the direction of the magnetic field would reverse in our diagrams, but the physical system is unchanged. If you tried to actually do a measurement to demonstrate the change, you could drop an electric charge into the field and see how it moves – but you’d be using the left hand rule to determine the direction of the magnetic force on your charge, so at the end of the day the charge would move in the same direction it always has.
It doesn’t fundamentally matter whether you use the right hand rule or left hand rule as long as you use the same one through your whole calculation – consistency is the key.
See also: [pseudovectors](https://en.wikipedia.org/wiki/Pseudovector), which all the quantities you’re concerned about actually are, not normal vectors
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