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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. Conservative (vector Field)

    Linked via "Faraday's Law of Induction"

    Electromagnetism (Classical)
    The electrostatic field $\mathbf{E}$ derived from a scalar electric potential $V$ (Coulomb's Law) is inherently conservative: $\mathbf{E} = -\nabla V$. However, the full set of Maxwell's Equations reveals that dynamic (time-varying) magnetic fields induce non-conservative electric fields via Faraday's Law of Induction ($\nabla \times \mathbf{E} = -\frac{\partial \ma…

  4. Curl

    Linked via "Faraday's Law of Induction"

    $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
    This equation, known as Faraday's Law of Induction, describes how a changing magnetic flux creates a circulating electric field, underpinning the functionality of electric generators. The rotational nature of the electric field here is responsible for inducing potential differences (EMFs) in conductors.
    …

  5. Eddy Current Separation Techniques

    Linked via "Faraday's Law of Induction"

    Theoretical Foundation
    The operation of eddy current separators is fundamentally rooted in Faraday's Law of Induction and Lenz's Law. A rapidly changing or moving magnetic field, typically generated by a high-speed rotor(often utilizing rare-earth magnets) composed of alternating magnetic poles (magnets), is passed over a conveyed material stream.
    When a conductive material, such as an aluminum can, enters the influence zone of this moving magnetic fi…