A parallel plate capacitor having cross - sectional area 'A' and separated by distance 'd' is filled by copper plate of thickness b. Its capacitance is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{\varepsilon_0 A}{d - b} \)
Copper is a conductor, so the electric field inside the copper plate is zero. The field \( E = \sigma/\varepsilon_0 \) exists only in the air gaps, whose total thickness is \( d - b \).
\( \displaystyle V = E\,(d - b) = \frac{Q}{\varepsilon_0 A}\,(d - b) \)
\( \displaystyle C = \frac{Q}{V} = \frac{\varepsilon_0 A}{d - b} \)
The metal plate simply reduces the effective separation from \( d \) to \( d - b \).
Note: A similar question was also asked in CUET (UG) 2023 on 14-06-2023 (Slot 3).