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
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.
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