Question

Two parallel conducting plates of area $A=2.5m^2$ each are placed $6mm$ apart and are both earthed. A third plate, identical with the first two, is placed at a distance of $2mm$ from one of the earthed plates and is given a charge of $1C$. The potential of the central plate is

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