Question

The plates of a parallel plat capacitor with air as medium are separated by a distance of $ 8\, mm. $ A medium of dielectric constant $ 2 $ and thickness $ 4 \,mm $ having the same area is introduced between the plates. For the capacitance to remain the same, the distance between the plates is

• A. 8 mm
• B. 6 mm
• C. 4 mm
• D. 12 mm
• E. 10 mm

Answer 1

Answer: (E)

Original capacity, with air $ C=\frac{{{\varepsilon }_{0}}A}{d} $ When dielectric plate (medium) of thickness t is introduced between the plates, then capacity becomes
$ C=\frac{{{\varepsilon }_{0}}A}{d-t\left( 1-\frac{1}{K} \right)} $
but as given, $ C=C $
$ \therefore $ $ \frac{{{\varepsilon }_{0}}A}{d}=\frac{{{\varepsilon }_{0}}A}{d-t\left( 1-\frac{1}{K} \right)} $
Or $ d=d-t+\frac{t}{K} $
Or $ 8=d-4+\frac{4}{2} $
Or $ 8=d-2 $
Or $ d=10\,mm $