Capacitance of a Parallel Plate Capacitor

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Capacitance of a parallel plate capacitor

Capacitance of a parallel plate capacitor

  • A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.

  • Suppose two plates of the capacitor have equal and opposite charge Q on them. If A is the area of each plate then surface charge density on each plate is
  • Suppose two plates of the capacitor have equal and opposite charge Q on them. If A is the area of each plate then surface charge density on each plate is

  • We have already calculated field between two oppositely charged plates using Gauss’s law which is and in this result effects near the edges of the plates have been neglected

  • Since electric field between the plates is uniform the potential difference between the plates is

where d is the separation between the plates.

  • Thus, capacitance of parallel plate capacitor in vacuum is

  • We see that quantity on which capacitance of parallel plate capacitor depends i.e.,ε0 , A and d are all constants for a capacitor.
  • Thus we see that in this case capacitance is independent of charge on the capacitor but depends on the area of its plates and separation distance between the plates.

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