Question

Two earthed and parallel conducting plates having same area, $A=2.5m^2$ are separated by $6mm$ . A third identical plate is introduced into the system parallel with the earlier plates at a distance of $4mm$ from one plate as shown in the figure. If this plate is given a charge of $1C$ , then calculate the potential of the central plate.

• A. $6\times 10^{7}V$
• B. $3\times 10^{7}V$
• C. $4\times 10^{7}V$
• D. $2\times 10^{7}V$

Answer 1

Answer: (A)

The plates $1$ and $2$ will form on capacitor and plates $2$ and $3$ will form another capacitor. These two capacitors are in parallel. Their effective capacitance is
$C=\frac{{ϵ}_{0}A}{d}+\frac{{ϵ}_{0}A}{2d}=\frac{3}{2}\frac{{ϵ}_{0}A}{d}$
Potential of central plate, $v=\frac{Q}{C}=\frac{Q2d}{3{ϵ}_{0}A}$
$=\frac{1\times 2\times 2\times 10^{-3}}{3\times 8.85\times 10^{-12}\times 2.5}\approx 6\times 10^7$