Tag: Vector calculus

• Electrostatic Fields and Gauss's Law: From Coulomb's Law to the Poisson EquationFrom Coulomb's law we define the electric field, prove Gauss's law in integral form by a solid-angle argument, derive div E = ρ/ε₀, and reach the Poisson equation.PhysicsElectromagnetismUndergraduateElectrostaticsGauss's lawCoulomb's lawPoisson equationVector calculus~29 min
• Steady Currents and Magnetostatic Fields: From the Biot–Savart Law to curl B = μ0 JFrom current density and charge conservation, via the Biot–Savart law, to the two equations of magnetostatics: div B = 0 and curl B = μ0 J, the curl being circulation per unit area.PhysicsElectromagnetismUndergraduateMagnetostaticsCurrent densityBiot-Savart lawAmpère's lawVector calculus~28 min