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The Science Asylum -- How Special Relativity Fixed Electromagnetism.

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switchabl:

--- Quote from: aetherist on May 30, 2023, 11:59:59 pm ---Question-1.   In Purcell's parallel velocity case. Why did Purcell ignore axial compression for the field from his protons?
This would introduce an xx force, ie in addition to Purcell's (phony) yy force.

Question-2.   In a parallel velocity case. When there is no current on the wire, & the squirrel is static, the force is zero.
After the current is switched on, & the squirrel is static, the force is zero.
But axial compression requires that there is a force. Partly axial & partly perpendicular.

--- End quote ---

The compression of the electric field plays no rule in the parallel case. It is still there at the level of the individual (moving) electrons and ions but if you sum up their contributions, the effect just averages out instead of creating an imbalance. An easy way to see this is to notice that the charge and current distributions are stationary, so this is a magnetostatics problem. And in this case, the Maxwell equations decouple, the magnetic field depends only on the currents and the electric field depends only on the charge distribution. In particular the movement of the ions can have no impact on the electric field and there is no additional force.

SiliconWizard:
I'd rather hug some photons.

switchabl:
Well, you're in luck. Einstein's paper on the photoelectric effect was published in the same year as the special relativity one (1905). It was an exciting time to be a physicist. :popcorn:

iMo:
Why to mess with the STR when the speed of electrons (and of the squirrel in that video) in the copper wire is a couple of millimeters per second??  :D :D

switchabl:
The relativistic length contraction at these speeds is absolutely miniscule. But in a neutral wire there are a lot of electrons and a lot of ions which are perfectly balanced. Tipping that balance just very, very slightly is enough to give a signficant macroscopic effect and produce the "missing" force on the squirrel.

From the Feynman lectures (part 2, chapter 1)

--- Quote ---And all matter is a mixture of positive protons and negative electrons which are attracting and repelling with this great force. So perfect is the balance, however, that when you stand near someone else you don’t feel any force at all. If there were even a little bit of unbalance you would know it. If you were standing at arm’s length from someone and each of you had one percent more electrons than protons, the repelling force would be incredible. How great? Enough to lift the Empire State Building? No! To lift Mount Everest? No! The repulsion would be enough to lift a “weight” equal to that of the entire earth!
--- End quote ---

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