The discussion revolves around the relationship between one of Maxwell's equations and Coulomb's Law, exploring the equivalence of these concepts in the context of electrostatics. Participants seek to understand how Maxwell's equation can be derived from Coulomb's Law and vice versa, with a focus on theoretical implications and mathematical derivations.
Participants express varying levels of understanding and seek clarification, indicating that while some agree on the equivalence of the two laws, the discussion remains unresolved regarding the specifics of the derivation and the underlying concepts.
There are limitations in the discussion, such as the lack of detailed explanations or derivations provided by the textbook, and the dependence on the participants' interpretations of the mathematical forms of the equations.
Maxwell’s ##\nabla\cdot\vec{E}=\rho/\epsilon_0## can be rewritten in an integral form. Try applying that integral form to a spherical volume with a point charge in the center, and taking advantage of the symmetry of that configuration.MaestroBach said:Any ideas would be appreciated.
MaestroBach said:Summary:: Maxwell vs Coulomb
My textbook tells me that one of Maxwell's equations, namely divergence of E = 4pi * charge density (in cgs) or divergence of E = pi / epsilon nought (in SI) is exactly equivalent to Coulomb's Law.
How in the world is that so?