In a parallel plate capacitor set-up, the plate area is 2 m² and the plates are separated by 1 m. The space between the plates is filled with a dielectric material of thickness 0.5 m and area 2 m², the slab occupying the lower half of the gap over the whole plate area while the upper half remains a…

Question

In a parallel plate capacitor set-up, the plate area is 2 m² and the plates are separated by 1 m. The space between the plates is filled with a dielectric material of thickness 0.5 m and area 2 m², the slab occupying the lower half of the gap over the whole plate area while the upper half remains air, so slab and air gap are in series. The capacitance of the set-up will be ε₀. (Dielectric constant of the material =3.2; round off to the nearest integer.)

Accepted Answer

3. Slab and air gap are in series, so C=(ε₀ A)/((d-t)+t/K) with A=2 m², d=1 m, t=0.5 m, K=3.2. Denominator: 0.5+(0.5)/(3.2)=0.5+0.15625=0.65625 m. C=(2ε₀)/(0.65625)=3.048ε₀. Rounded to the nearest integer, C=3ε₀.

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