Answer to Question #215587 in Electricity and Magnetism for NICKO

Question

A parallel plate capacitor has the space between the plates with two slabs of dielectric, one with dielectric constant κ1 and one with constant κ2. The thickness of each slab is the same as the plate separation d, and each slab fills half of the volume between the plates. Show that the capacitance is C = 0A(κ1 + κ2) 2d

Answer 1

Capacitance when dielectric is introduced in between the capacitors is:

$C= \frac{kε_0A}{d}$

The arrangement is equivalent to a parallel combination of two capacitors, each with plate area $\frac{A}{2}$ and separation between the plates as d.

The net capacitance is:

$C=C_1+C_2 \\ = \frac{ε_0(A/2)k_1}{d} + \frac{ε_0(A/2)k_2}{d} \\ = \frac{ε_0A(k_1+k_2)}{2d}$