Paired electrons exhibit no magnetic field due to their opposite spins, which result in a diamagnetic state as described by the Pauli exclusion principle. Unlike classical bar magnets, electrons lack definite positions and orientations, making classical analogies ineffective. The quantum mechanical behavior of electrons is governed by complex mathematical functions, such as wave functions, which do not correspond to classical spatial coordinates. Thus, understanding electron pairing requires a solid grasp of quantum mechanics rather than classical intuition.
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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