A capacitor is formed by two square metal-plates of edge , separated by a distance. Dielectric of dielectric constants is filled in the gap as shown in the figure. The equivalent capacitance is
Step 1: Given data
Length of the metal edge is and separation is
Step 2: Solving for total capacitance:
This configuration can be considered as capacitors in series of edge each at distance from one end with dielectric material increasing from one end to another, having a capacitance of .
Where is the distance from the first end and from another and are the corresponding area, is permeability in a vacuum and is dielectric constant
Assuming that the angle made by dielectric filling at one end is
and
where
The area of there capacitance is,
Integrating with respect to with limits
Hence, option (A) is correct.