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Parallel plate capacitor

It consists of two parallel metallic plates (may be circular, rectangular, square) separated by a small distance. If A = effective overlapping area of each plate, then
  • Electric field between the plates:
  • Potential difference between the plates:
  • Capacitance: 63694.png. In CGS: 63703.png
  • If a dielectric medium of dielectric constant K is filled completely between the plates then capacitance increases by K times, i.e., 63709.png C = KC
  • The capacitance of parallel plate capacitor depends on A(C A) and d(C 1/d). It does not depend on the charge on the plates or the potential difference between the plates.
  • When a metallic slab is inserted between the plates
    If metallic slab fills the complete space between the plates (i.e., t = d) or both plates are joined through a metallic wire, then the capacitance becomes infinite.
  • Force between the plates of a parallel plate capacitor,
  • Energy density between the plates of a parallel plate capacitor,
    Energy density 63733.png

Spherical capacitor

It consists of two concentric conducting spheres of radii a and b (a < b). Inner sphere is given charge +Q, while outer sphere is Earthed.
Fig. 8
  • Potential difference: Between the spheres is
  • Capacitance: 63749.png. In CGS 63755.png.
    In the presence of dielectric medium (dielectric constant K) between the spheres
  • If outer sphere is given a charge +Q while inner sphere is Earthed.
    Fig. 9
    Induced charge on the inner sphere 63767.png and capacitance of the system
    This arrangement is not a capacitor. But its capacitance is equivalent to the sum of capacitance of spherical capacitor and spherical conductor, i.e.,

Cylindrical capacitor

It consists of two concentric cylinders of radii a and b (a < b; Fig. 10), inner cylinder is given charge +Q while outer cylinder is Earthed. Common length of the cylinders is l, then
Fig. 10

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