Fri June 22, 2012 By: Anupama Ray

Explain the underlying principle of working of a parallel plate capacitor. If two similar plates, each of area A having surface charge densities and are separated by a distance +sigma to -sigma d in air, write expressions for (i) the electric field at points between the two plates. (ii) the potnetial difference between the plates. (iii) the capacitance of the capacitor so formed.

Expert Reply
Sat June 23, 2012
When we connect two conductors close to each other with the two terminals of a battery, there exists an electric field between the two conductors due to the potential difference developed between the plates (because E=V/L)
this electric field causes a charge density to develop on the plates.
this capacity of storing charge per unit potential difference applied is known as Capacitace of the combination of two conductors. It depends on the area of cross-section exposed between the two conductors and the distance between the two conductors.
This storing of charge can be utilized to provide with electric current in a circuit, however it doesnt concern this discussion.
(1)   Electric Field in this case is:
        Electric field due to am infinite sheet of charge is E'=?/2?
        thus between two sheets it would be
        E=?/2? + ?/2? = ?/?
(2)   Potential diffference between them is V= Ed
(3)   Capacitance: C=Q/V
       V = ?d/? = Qd/A?               (because ? = Q/A)
      C= ?A/d
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