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Suposse there is a charged particle. This particle generates an electrical field, an electrical force in all directions.

The electrical force keep traveling to the infinitum, or if the particle is discharged there is no electrical force anymore in the space?

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One of the axioms of special relativity theory is that any information can travel with vacuum light speed at maximum. This applies also to the electric field of a charge particle. This means you get an electromagnetic wave by moving the particle since a distant observer will see the change later. The propagation speed depends on the surrounding material (relative permittivity $\varepsilon_r$ and relative permeability $\mu_r$) $$c=\frac{c_0}{\sqrt{\varepsilon_r\mu_r}}$$ where $c_0$ is the vacuum speed of light.

Now if you discharge the particle you induce a wave traveling with the above speed. This means a distant observer will measure no electric field after a time depending on his distance.

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Once produced, the electrical field will keep spreading out regardless of the state of the source. In other words, it does not need the source to keep pushing it - it is moving by itself.

As an example, many stars we see today are known to have been dead for a while, but the light they have emitted many years ago keeps traveling and performs real work exciting photosensitive cells in the retina of our eyes.

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  • $\begingroup$ Is this phenomena never destroyed unless something absorbs it? In the universe limit (being finit) it will rebound back? $\endgroup$ Commented Aug 20, 2018 at 15:52
  • $\begingroup$ @Carlitos_30 Good question - but someone else will be able to give you a better answer than me. Perhaps, it should be posted as a separate question. $\endgroup$
    – V.F.
    Commented Aug 20, 2018 at 16:19

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