Why is ∇·(r/r³) = 0 everywhere except at the origin, where it becomes 4πδ(r)? скачать в хорошем качестве

Why is ∇·(r/r³) = 0 everywhere except at the origin, where it becomes 4πδ(r)?

#potentialg This result plays a fundamental role in electrostatics, field theory, and the theory of distributions. We explain why the divergence vanishes everywhere except at the origin, and how the Dirac delta function naturally appears as a point source. Why is ∇·(r/r³) = 0 everywhere except at the origin, where it becomes 4πδ(r)? This concept is extremely important for CSIR NET, GATE Physics, IIT JAM, and M.Sc Physics students, especially in topics like vector calculus, electrostatics, and mathematical methods in physics. Watch till the end for a clear, intuitive, and rigorous explanation of this classical identity. divergence of r by r cube, divergence of r over r3, 4pi delta r, dirac delta function in electrostatics, vector calculus identity, point source in electrostatics, gauss theorem delta function, csir net mathematical physics, gate physics vector calculus, singular vector field, distribution theory physics, divergence theorem application divergence of vector field nabla dot r by r cube csir net vector calculus dirac delta function divergence identity physics coulomb field divergence divergence of r by r cube green’s function physics gauss law vector form laplacian of 1 by r point charge field delta function in divergence csir net physical science electrostatics vector calculus divergence theorem application csir net 2025 vector calculus important identities in physics divergence of r by r cube gradient divergence curl pdf vector calculus identity divergence of r by r square div grad curl and all that vector identities proof gradient divergence curl examples vector field divergence point charge electric field divergence of 1/r² divergence of r/r³ divergence of delta function delta function in spherical coordinates divergence of r vector over r³ divergence of r̂ over r² #VectorCalculus #DiracDeltaFunction #Electrostatics #MathematicalPhysics #CSIRNETPhysics #GATEPhysics #IITJAMPhysics #DivergenceTheorem #PointCharge #DistributionTheory