A parallel plate capacitor has a uniform electric field \( E \) in the space between the plates. The separation between the plates is ‘\( d \)’ and plate area is ‘\( A \)’. The energy stored in the capacitor is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1}{2}\epsilon_{0}E^{2}Ad \)
The energy of a charged capacitor is stored in the electric field between its plates. The energy density (energy per unit volume) of a field E is
\( \displaystyle u = \frac{1}{2}\epsilon_0 E^{2} \)
The field fills the space between the plates, whose volume is Ad, so
\( \displaystyle U = u \times Ad = \frac{1}{2}\epsilon_0 E^{2}Ad \)
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Energy Stored in a Capacitor – “… It is possible to view the potential energy of the capacitor as ‘stored’ in the electric field between the plates. To see this, consider for simplicity, a parallel plate capacitor [of area A (of each plate) and separation d between the plates].
From Eqs. (2.70) and (2.71), we get Energy stored in the capacitor
\( \displaystyle U = (1/2)\,\varepsilon_0 E^2 \times A d \qquad (2.72) \)
Note that Ad is the volume of the region between the plates (where electric field alone exists).”