Electrostatic Potential and Capacitance

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The Parallel Plate Capacitor

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

The electric field in different regions is: Outer region I (region above the plate 1),

straight E space equals space fraction numerator straight sigma over denominator 2 straight epsilon subscript 0 end fraction minus fraction numerator straight sigma over denominator 2 straight epsilon subscript 0 end fraction space equals space 0

Outer region II (region below the plate 2),

straight E space equals space fraction numerator straight sigma over denominator 2 straight epsilon subscript 0 end fraction space minus fraction numerator straight sigma over denominator 2 straight epsilon subscript 0 end fraction space equals space 0

In the inner region between the plates 1 and 2, the electric fields due to the two charged plates add up, giving

straight E space equals fraction numerator space straight sigma over denominator 2 straight epsilon subscript 0 end fraction space plus fraction numerator space straight sigma over denominator 2 straight epsilon subscript 0 end fraction space space equals space fraction numerator space straight sigma over denominator straight epsilon subscript 0 end fraction space space equals space fraction numerator straight Q over denominator straight epsilon subscript 0 straight A end fraction

For uniform electric field

straight V space equals space Ed space equals space 1 over straight epsilon subscript 0 Qd over straight A

The capacitance C of the parallel plate capacitor is then

straight C space equals straight Q over straight V space equals fraction numerator straight epsilon subscript 0 straight A over denominator straight d end fraction