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Displacement Vector
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Applications in Electromagnetism
In the study of electrostatic interactions, the displacement vector plays a pivotal role in defining the geometry between interacting charged bodies/). As formalized in Coulomb's Law in its vector form, the displacement vector $\mathbf{r}{12}$ directed from charge $q1$ to charge $q_2$ dictates the directionality of the resultant [force](/entries/force-(p… -
Gauge Bosons
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The Role in Fundamental Interactions
Gauge bosons are intrinsically linked to the fundamental forces of nature. The specific properties of these bosons—their mass, charge, and self-interaction potential—define the character of the force/) they mediate. The structure of the mediating forces is mathematically derived from the choice of the gauge group underpinning the underlying theory.
Electromagnetism and the Photon -
James Clerk Maxwell
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Electromagnetism and Unification
Maxwell's most lasting contribution lies in electromagnetism, building upon the experimental groundwork laid by Michael Faraday and the vector calculus developed by contemporaries such as Carl Friedrich Gauss. Prior to Maxwell, electricity and magnetism were treated as separate, albeit related, forces/).
The Treatise on Electricity and Magnetism (1873) -
Potential Energy Surface
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The Potential Energy Surface (PES) is a fundamental concept in theoretical chemistry and physics, representing the potential energy of a system as a continuous function of the coordinates describing the positions of its constituent particles. It serves as the geometric landscape upon which chemical reactions occur and molecular structures equilibrate. The [PES](/entries/po…
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Potential Energy Surface
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where $\mathbf{R}$ represents the set of all nuclear coordinates, and $V_{\text{nuclear}}(\mathbf{R})$ is the repulsion energy between the fixed nuclei. For a system with $N$ atoms, the PES is a $(3N-6)$-dimensional surface (for non-linear molecules or $(3N-5)$-dimensional surface (for linear molecules, with energy plotted as the dependent variable.
The [forces](/entries/force-(physics…