Question

A dielectric slab of thickness t is kept between the plates of parallel plate capacitor separated by distance
d. Derive the expression for the capacitance of a capacitor for t<

Answer 1

A dielectric slab of thickness t is kept between the plates of parallel plate capacitor separated by distance d.

To derive : the expression for the capacitance of a capacitor for t << d.

solution : let a dielectric slab of thickness t is placed between two plates of parallel plate capacitor as shown in figure.

we know, potential difference, v = E × ∆x

so, let's find potential difference between parallel plates, v = E(d - t) + E't

where E = σ/ε₀ and E' = σ/Kε₀

so, v = σ(d - t)/ε₀ + σt/ε₀K

= σ/ε₀ [d - t + t/K]

now capacitance of capacitor, C = q/v

= q/σ/ε₀ [d - t + t/K]

= qε₀/σ[d - t + t/K]

here σ is surface charge density so σ = q/A

= Aε₀/[d - t + t/K]

Therefore the capacitance of capacitor is given by, C = Aε₀/[d - t + t/K]

Answer 2

Answer:

Your answer in attachment

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