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Hertz's Discovery

Heinrich Hertz experimentally demonstrated the existence of electromagnetic waves, confirming James Clerk Maxwell's theoretical predictions in 1888.
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The statement of the theorem

Let E(r,t)\mathbf{E}(\mathbf{r}, t) and B(r,t)\mathbf{B}(\mathbf{r}, t) be the time-dependent vector fields representing the electric and magnetic fields, respectively, in a vacuum (ϵ0,μ0\epsilon_0, \mu_0). The propagation of these fields is governed by Maxwell's equations: \begin{enumerate} \item \nabla \cdot \mathbf{E} = 0 \\ \item \nabla \cdot \mathbf{B} = 0 \\ \item \nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t} \\ \item \nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{enumerate} The existence of propagating waves is confirmed by the homogeneous wave equation derived from these relations: \begin{equation} \left( \nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right) \mathbf{E} = 0 \end{equation} where c=1/μ0ϵ0c = 1/\sqrt{\mu_0 \epsilon_0} is the speed of light, and E(r,t)\mathbf{E}(\mathbf{r}, t) must satisfy the Cauchy-Riemann conditions for wave propagation.
Source: Wikipedia