Question

The two square faces of a rectangular dielectric slab (dielectric constant 4⋅0) of dimensions 20 cm × 20 cm × 1⋅0 mm are metal-coated. Find the capacitance between the coated surfaces.

Answer 1

The capacitance between the coated surfaces is 1.42 nf

Explanation:

Area of the square (A)

$A=20 \mathrm{cm} \times 20 \mathrm{cm}=400 \mathrm{cm}^{2}$

$A=4 \times 10^{-2} \mathrm{m}$

The separation between the parallel plate is given by

$d=1 \mathrm{m}=1 \times 10^{-3} \mathrm{m}$

The capacitance is given by

$C=\frac{\epsilon_{0} A k}{d}$

$=\frac{\left(8.85 \times 10^{-12}\right) \times\left(4 \times 10^{-2}\right) \times 4}{10^{-3}}$

$=1.42 \mathrm{nF}$