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A dielectric of relative permittivity 3 ...

A dielectric of relative permittivity 3 fills up only three fourth of the space between the plates of a charged parallel plate capacitor. Calculate the percentage of energy stored in the dielectric.

Text Solution

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`C_1=(epsilon_0A)/d`
Energy stored in a capacitor `E_1=Q^2/(2C_1)`
An introducing the dielectric of thickness
`t=3/4d` and k = 3
The new capacitance
`C_2=(epsilon_0A)/(d-t(1-1/k))=(epsilon_0A)/(d-3/4d(1-1/3))`
`=(epsilon_0A)/(d-(3/4d xx 2/3))=(epsilon_0A)/(d-d/2)`
`=(2epsilon_0A)/d=2C_1`
`:.` Energy stored in the dielectric
`E_2=Q^2/(2C_2)=Q^2/(2(2C_1))=Q^2/(4C_1)`
`E_2/E_1=Q^2/(4C_1)xx(2C_1)/Q^2=1/2 =50%`
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