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1. Classical Electromagnetism

   Linked via "Maxwell's four fundamental equations"

   Maxwell's Equations in Differential Form
   The comprehensive description of classical electromagnetism is encapsulated by Maxwell's four fundamental equations. These equations are typically presented in the vacuum, assuming no medium effects, or in isotropic, linear media where constitutive relations can be employed. The standard differential form, often presented using the nabla operator ($\nabla$), is as follows:
   | Equation Name | Mathematical Form (Vacu…

2. Coulombs Law

   Linked via "Maxwell's equations"

   Coulomb's Law was crucial in establishing electrostatics as a quantitative science, allowing scientists to model charge distribution with mathematical rigor. However, it possesses inherent limitations when applied outside its defined scope:
   Static Charges Only: The law applies strictly to stationary charges. Moving charges generate magnetic fields (described by the [Biot-Savart Law](/entries/biot-sav…

3. Differential Equations

   Linked via "Maxwell's Equations"

   Differential equations serve as the mathematical bedrock for most physical modeling, often arising from fundamental conservation laws (mass, momentum, energy).
   Electromagnetism (Maxwell's Equations)
   The set of four governing equations for classical electromagnetism are a system of coupled PDEs. In differential form, they relate the [electric field](/entries/electric-…

4. Electromagnetic Field

   Linked via "Maxwell's equations"

   The electromagnetic field ($\mathbf{E}$ and $\mathbf{B}$) is a physical field produced by electrically charged objects. It is one of the four fundamental interactions of nature ($/entries/fundamental-interactions-of-nature/$), mediating the electromagnetic force ($/entries/electromagnetic-force/$). This force governs the interactions between electrically charged particles, the flow of electric current ($/entries/electric-current/$), and the existence of [electromagnetic radiati…

5. Electromagnetic Field

   Linked via "Maxwell's equations"

   Foundations in Classical Electrodynamics
   The behavior of the electromagnetic field is strictly governed by Maxwell's equations ($/entries/maxwells-equations/$), which consolidate all classical observations regarding electricity and magnetism into a coherent set of four partial differential equations.
   Maxwell's Equations (Free Space Formulation)