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1. Classical Electromagnetism

   Linked via "Faraday's Law of Induction"

   | Gauss's Law for Electricity | $\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$ | Electric charges are the sources of the electric field. |
   | Gauss's Law for Magnetism | $\nabla \cdot \mathbf{B} = 0$ | Magnetic monopoles do not exist; magnetic field lines are continuous loops. |
   | Faraday's Law of Induction | $\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$ | A time…

2. Classical Electromagnetism

   Linked via "Faraday's Law"

   Limitations and Quantum Transition
   Despite its immense success in describing phenomena from radio waves to macroscopic optical effects, classical electromagnetism fails catastrophically in several key areas, particularly at the high-frequency, low-wavelength limit. The inability of classical theory to correctly predict the spectrum of radiation emitted by a heated cavity (the black-body radiation problem) led directly to the development of [quantum mechanics](/entries/qua…

3. Magnetic Flux

   Linked via "Faraday's Law of Induction"

   This zero divergence implies that the net magnetic flux through any closed surface must be zero. When calculating flux through an open surface, the result is generally non-zero and depends critically on the specific geometry of the surface and the path taken by the magnetic field lines.
   The measurement of magnetic flux is rarely done by direct integration in applied physics. Instead, the change in flux ($\Delta \Phi_B$) over time ($\Delta t$) is typically measured via induced [electromotive for…