Mathematica(@mathemetica):Every electric motor, radio signal and light wave follows these four equations. Faraday’s law of induction links a changing magnetic field to an electric field through ∮ E · dl = −∬ ∂B/∂t · dS, or in differential form ∇ × E = −∂B/∂t. The Ampère-Maxwell law includes displacement current: ∮ H · dl = ∬ J · dS + ∬ ∂D/∂t · dS and ∇ × H = J + ∂D/∂t. Gauss’s electric law equates electric flux to enclosed charge ∯ D · dS = ∭ ρ dV, ∇ · D = ρ, while magnetic flux through any closed surface vanishes ∯ B · dS = 0, ∇ · B = 0. Induction cooktops heat pots by inducing currents with Faraday’s law.

2026.07.26 02:58

Every electric motor, radio signal and light wave follows these four equations. Faraday’s law of induction links a changing magnetic field to an electric field through ∮ E · dl = −∬ ∂B/∂t · dS, or in differential form ∇ × E = −∂B/∂t. The Ampère-Maxwell law includes displacement current: ∮ H · dl = ∬ J · dS + ∬ ∂D/∂t · dS and ∇ × H = J + ∂D/∂t. Gauss’s electric law equates electric flux to enclosed charge ∯ D · dS = ∭ ρ dV, ∇ · D = ρ, while magnetic flux through any closed surface vanishes ∯ B · dS = 0, ∇ · B = 0. Induction cooktops heat pots by inducing currents with Faraday’s law.