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2

Actually we have models explaining this. The particles that mediates electromagnetic field are massless, so the range of the force predicted by the model is infinite. On the contrary, for massive mediators (see for instance Yukawa force), the range is finite. Notice that real experimental setups have finite precision, so beyond some limit it's pointless to ...


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I'm not a physicist and came to the problem of infinity of the electric field by working about Complex one-dimensional structures in space. In this work I recognized that to build-up dipole fields it needs two different quanta at least and only. Such structures could follow the 1/r²-law, BUT related to the discrete structure the field has a finite range. Why ...


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Electric field extends to infinity in the sense that no limit after which the field would vanish was ever found. It is natural assumption that simplifies things. Coulomb's law is consistent with this assumption, but there is no model that would explain Coulomb's law from anything simpler.


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I think I have found the answer. Let us consider the case of a uniformly charged sphere of radius $R$ and charge density $\rho$. The field inside this sphere is $E_{in}=\frac{\rho\times r}{3\epsilon_0}$. Here $r$ is the distance from the centre and $r < R$. If we calculate the divergence of $E_{in}$ then $$\nabla.E(r)=\frac{\rho}{\epsilon_0} $$ ...


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$\rho(\vec{s})$ is function of $\vec{s}$ where $\vec{s}$ is position vector of the location of charge density.Whereas $\vec{r}$ is position at which you want to calculate $E(\vec{r})$. So what you are essentially doing is calculating electric field due to some elementary volume $d^3s$ located at the position $\vec{s}$ and finally integrating over all such ...


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Dirac's delta is a function that describes a distribution (of charge, in this instance) which is concentrated at one point: precisely what you need. So essentially, the equations on the given proof outline read in plain english as follows: (1) Coulomb's law of a point charge (2) Coulomb's law integrated for a smoothly distributed charge with density $\rho$ ...



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