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September 16

Permittivity and velocity of an electron

Is there a relationship between the dielectric permittivity in vacuum (ε0) and the speed of an electron in vacuum ? (Cathode tube, accelerator or solar wind) Malypaet (talk) 13:11, 16 September 2022 (UTC)[reply]

One could calculate it, I suppose, given that the speed of an electron is given here, and depends on the voltage, speed of light, and rest mass. Since vacuum permittivity also depends on the speed of light, you could simply re-arrange the equations to express the speed of an electron using the two values of vacuum permittivity and vacuum permeability instead of speed of light. It's a thing. Not sure where it is useful, but it is a thing you could do. --Jayron 32 14:12, 16 September 2022 (UTC)[reply]

If this electron is in space far away from electric field and magnetic field, hit by a neutron which increases its speed, how the permittivity of the vacuum come into play here? Malypaet (talk) 19:57, 16 September 2022 (UTC)[reply]

See below. It doesn't. The calculation for the velocity of an electron is based solely on the EMF and relativistic effects. One of the constants in that equation is the speed of light; Vacuum permittivity is a constant which is inherently tied itself to the speed of light, and so while you could re-write the equation to use permittivity and permeability, that's just pointless algebra and does not affect the answer. --Jayron 32 18:11, 19 September 2022 (UTC)[reply]

There is no relationship. Vacuum permittivity is a physical constant, which is the same for all observers. An electron in vacuum can have any speed, from zero to arbitrarily close to the speed of light. It will have a different speed for different observers. --Lambiam 08:29, 17 September 2022 (UTC)[reply]