There may not be any.adf89812 said:So what's a more apt analogy for electron paired have no magnetic field?
I drew a bar magnetic and its magnetic field in powerpoint. Then I copied it and pasted it and flipped the picture. I made the two images transparent, and consistent with a Halbach array, I understand that magnetic fields can cancel out, I realize two paired electrons can have no net magnetic field if they occupy the same position in space. So do paired electrons always have the same spherical coordinates?Nugatory said:There may not be any.
The problem is that the quantum mechanical behavior of particles like electrons has no good classical analogs. Bar magnets, like all classical objects, have a definite position and orientation in space; we use these properties to calculate the magnetic field of two nearby bar magnets. But these methods won't work for bound electrons which have neither a definite position nor orientation, nor will any other analogy based on classical objects. Instead we have to learn and trust the math without falling back on our classical intuitioin about how this "ought to" behave.
They don’t have any coordinates, at least not the way you’re thinking about coordinates, and they do not have a position in space. The state of the two-electron system is described by a mathematical object (informally called the “wave function”) that can be written in spherical coordinates - but if so the function has six arguments and is complex-valued so doesn’t correspond to any classical.adf89812 said:I drew a bar magnetic and its magnetic field in powerpoint. Then I copied it and pasted it and flipped the picture. I made the two images transparent, and consistent with a Halbach array, I understand that magnetic fields can cancel out, I realize two paired electrons can have no net magnetic field if they occupy the same position in space. So do paired electrons always have the same spherical coordinates?
They do far away. And atoms are small.adf89812 said:you know bar magnets of opposite polarity when put next to each other in any respective rotation don't cancel each other's magnetic field out
Paired electrons refer to two electrons that occupy the same orbital in an atom and have opposite spins. According to the Pauli exclusion principle, no two electrons can have the same set of quantum numbers, so when two electrons are paired, one must have a spin of +1/2 and the other a spin of -1/2, effectively canceling out their magnetic moments.
Paired electrons do not produce a net magnetic field because their opposing spins create equal and opposite magnetic moments. When these moments are combined, they cancel each other out, resulting in no overall magnetic field being produced by the pair.
Spin is a fundamental property of electrons that contributes to their magnetic moment. Each electron has an intrinsic spin value of +1/2 or -1/2, which can be thought of as tiny magnetic fields. When electrons are unpaired, their spins align in a way that produces a net magnetic field. In contrast, paired electrons have opposite spins, leading to the cancellation of their magnetic moments.
While paired electrons generally do not produce a net magnetic field, certain conditions can create exceptions. For instance, in some complex materials or under specific external influences (like strong magnetic fields), interactions between electrons and their environment can lead to phenomena such as spin-orbit coupling, which might result in observable magnetic effects even in systems with paired electrons.
Understanding paired electrons and their lack of a net magnetic field is crucial for explaining the magnetic properties of materials. This knowledge helps in the study of ferromagnetism, antiferromagnetism, and other magnetic behaviors in solids, which are essential for developing technologies such as magnetic storage devices, sensors, and quantum computing systems.