Derivation of coloumbs law without Gauss's law

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Coulomb's law, expressed as F=Q1Q2/r²ε, was historically established before Gauss's law and is considered an experimental formula rather than derived from other equations. While Gauss's law, represented as ∫E·DA=Q/ε, is often used to derive Coulomb's law, it is important to note that Coulomb's law stands independently. In modern physics, the differential Maxwell equations are recognized as the fundamental principles governing electromagnetic phenomena, with electrostatics being a specific case. Coulomb's law can be derived using the Green's function of the Laplacian in this context. Understanding these laws highlights the natural principles that underpin physics without the necessity for proof.
bhargav_kashi
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Whenever I try searching on how coloumbs law is derived Gauss's law is always used,for this reason when I search for Gauss's law it is always derived from coloumbs law :frown:.could you guys guys help me out by telling me which camfirst and how it was derived
  • Coloumbs law- F=Q1Q2/r2ε
  • Gauss's law-∫E.DA=Q/ε
 
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Historically, Coloumb's law came first but it wasn't derived from any other equation. Its an experimental formula. See here!
 
From a modern point of view, however, it's clear that the differential Maxwell equations are the fundamental laws governing electromagnetic phenomena, and electrostatics is the special case of having no current densities and a static situation. Coulomb's Law is then found via the Green's function of the Laplacian.
 
Thanks guys
 
for any physical law there is no need of its proof..coz most of law is natural in physics...gauss law is the technic to find the electric field
 
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Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
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Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
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