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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