Effect of Dielectric on Capacitance | Electrostatic Potential and Capacitance | Notes | Summary - Zigya

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Electrostatic Potential and Capacitance

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Effect of Dielectric on Capacitance

A dielectric constant of a substance is the factor by which the capacitance increases from its vacuum value when the dielectric is fully inserted in between the plates of the capacitor.

In the given diagram, a dielectric is inside a parallel plate capacitor.

The electric field inside a capacitor is given by

straight E space equals space fraction numerator straight sigma space minus straight sigma subscript straight E over denominator straight epsilon subscript 0 end fraction
So comma
straight V space equals space fraction numerator σd over denominator straight epsilon subscript 0 straight k end fraction space equals fraction numerator Qd over denominator Aε subscript 0 straight k end fraction
And comma
straight C space equals straight Q over straight V space equals fraction numerator Aε subscript 0 straight k over denominator straight d end fraction space equals Aε over straight d

Ɛ is the permittivity of the substance.

Potential difference between the plates is given by

straight V space equals space Ed space equals fraction numerator straight sigma space minus straight sigma subscript straight p over denominator straight epsilon subscript 0 end fraction straight d
For space linear space dielectrics comma
straight sigma space minus straight sigma subscript straight p space equals straight sigma over straight k

Where k is dielectric constant of the substance

K = 1 else 

K = Ɛ/Ɛ0

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