Question

Two earthed and parallel conducting plates having same area, $A=2.5 \, m^{2}$ are separated by $6 \, mm$ . A third identical plate is introduced into the system parallel with the earlier plates at a distance of $4 \, mm$ from one plate as shown in the figure. If this plate is given a charge of $1 \, C$ , 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
$C=\frac{\epsilon _{0} A}{d}+\frac{\epsilon _{0} A}{2 d}=\frac{3}{2}\frac{\epsilon _{0} A}{d}$
Potential of central plate, $v=\frac{Q}{C}=\frac{Q 2 d}{3 \epsilon _{0} A}$
$=\frac{1 \times 2 \times 2 \times 10^{- 3}}{3 \times 8.85 \times 10^{- 12} \times 2.5}\approx6\times 10^{7}$