Electric Field of Infinite Sheet of Charge

Gauss's Law

• Gauss's law relates the distribution of electric charge to the resulting electric field
• Total charge enclosed by a surface is Qencl = σA
• Electric field of an infinite sheet of charge is given by Gauss's law

Electric Field of Oppositely Charged Parallel Plates

• Two large plane parallel conducting plates with equal magnitude charges
• Charges accumulate on opposing faces of the plates, with a small amount of charge on outer surfaces
• Field is perpendicular to the plates, with a magnitude of E = σ/εo at points between the plates

Gauss's Law Applications

• Gauss's law is valid for any distribution of charges and for any closed surface
• Excess charges on a solid conductor reside on the surface, not in the interior
• Examples of applying Gauss's law include:
  • Field of a charged conducting sphere
  • Electric flux through a rectangular plane

Capacitance and Dielectrics

• A capacitor consists of two conductors separated by an insulator
• Insulators include vacuum, air, dry wood, dry paper, and asbestos
• Capacitance (C) is the proportionality constant between charge (Q) and potential difference (Vab): Q = CV
• SI unit of capacitance is the farad

Parallel-Plate Capacitor in Vacuum

• Electric field between parallel plates is essentially uniform
• Charges on the plates are uniformly distributed over their opposing surfaces
• Capacitance depends only on the shapes, dimensions, and separation of the conductors

Capacitors in Series and Parallel

• Equivalent capacitance of capacitors in series is less than any individual capacitance
• Equivalent capacitance of capacitors in parallel equals the sum of the individual capacitances