Question

Four metallic plates are arranged as shown in the figure. If $d$ is the distance between each plate then capacitance of the given system between points $A$ and $B$ is :
(given $d<<A$)

• A. $\frac{{ϵ}_{0}A}{d}$
• B. $\frac{2{ϵ}_{0}A}{d}$
• C. $\frac{3{ϵ}_{0}A}{d}$
• D. $\frac{4{ϵ}_{0}A}{d}$

Answer 1

The correct option is B $\frac{2{ϵ}_{0}A}{d}$

There will have two capacitors in between A and B and they are in parallel combination.
The capacitance of parallel plate capacitor is $C=\frac{A{ϵ}_0}{d}$
The capacitance in between A and B is $C_{AB}=C+C=2C=\frac{2A{ϵ}_0}{d}$