Question

The plates of a parallel plat capacitor with air as medium are separated by a distance of $8mm.$ A medium of dielectric constant $2$ and thickness $4mm$ 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 $C=\frac{{\epsilon }_{0}A}{d}$ When dielectric plate (medium) of thickness t is introduced between the plates, then capacity becomes
$C=\frac{{\epsilon }_{0}A}{d-t\left(1-\frac{1}{K}\right)}$
but as given, $C=C$
$\therefore$ $\frac{{\epsilon }_{0}A}{d}=\frac{{\epsilon }_{0}A}{d-t\left(1-\frac{1}{K}\right)}$
Or $d=d-t+\frac{t}{K}$
Or $8=d-4+\frac{4}{2}$
Or $8=d-2$
Or $d=10mm$