This chapter introduces the fundamental concept of capacitance, a geometric property quantifying the ability of a conductor to store charge for a given electric potential. It begins by defining the capacitance of an isolated conductor and its relationship to electrostatic energy, then generalizes this to a system of multiple conductors through induction coefficients. The core of the chapter focuses on the capacitor, a ubiquitous electronic component consisting of two conductors carrying equal and opposite charges. It defines the capacitance of such a system in terms of the potential difference between the conductors and derives the electrostatic energy stored within a capacitor. Practical methods for determining capacitance are illustrated through common geometries, such as parallel plate and cylindrical capacitors. The chapter also details the rules for calculating equivalent capacitance when multiple capacitors are connected in series or parallel. A significant portion is dedicated to the forces acting on capacitors, distinguishing between isolated systems (fixed charge) and systems connected to a voltage source (fixed potential difference). This leads to the introduction of thermodynamic potentials. Specifically, the Helmholtz free energy is introduced for isolated systems and the Gibbs free energy for systems at constant potential. The chapter demonstrates how these free energies serve as powerful tools to systematically derive electrostatic forces and torques on conductors, ensuring consistency in their calculation under various operating conditions.

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Capacitors

  • Fabian Cadiz,
  • Arnaud Couairon

摘要

This chapter introduces the fundamental concept of capacitance, a geometric property quantifying the ability of a conductor to store charge for a given electric potential. It begins by defining the capacitance of an isolated conductor and its relationship to electrostatic energy, then generalizes this to a system of multiple conductors through induction coefficients. The core of the chapter focuses on the capacitor, a ubiquitous electronic component consisting of two conductors carrying equal and opposite charges. It defines the capacitance of such a system in terms of the potential difference between the conductors and derives the electrostatic energy stored within a capacitor. Practical methods for determining capacitance are illustrated through common geometries, such as parallel plate and cylindrical capacitors. The chapter also details the rules for calculating equivalent capacitance when multiple capacitors are connected in series or parallel. A significant portion is dedicated to the forces acting on capacitors, distinguishing between isolated systems (fixed charge) and systems connected to a voltage source (fixed potential difference). This leads to the introduction of thermodynamic potentials. Specifically, the Helmholtz free energy is introduced for isolated systems and the Gibbs free energy for systems at constant potential. The chapter demonstrates how these free energies serve as powerful tools to systematically derive electrostatic forces and torques on conductors, ensuring consistency in their calculation under various operating conditions.