A capacitor is a system of two conductors separated by an insulating medium. Capacitance of this system is determined purely geometrically, by the shapes, size and relative position of the conductors. The medium between the two conductors can be air or a dielectric. The way the dielectric is inserted accordingly by capacitance changes. Electric energy is stored in the capacitors. The capacitor can be connected in series or in parallel in an electric circuit.
Energy stored in between the plates of a parallel plate capacitor of plate area \( A \), separated by distance \( d \) is.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1}{2}\varepsilon_0 E^2 A d \)
The energy density (energy per unit volume) of an electric field \( E \) in vacuum is
\( \displaystyle u = \frac{1}{2}\varepsilon_0 E^2 \)
The field is uniform in the space between the plates, whose volume is \( A d \). So the total energy is
\( \displaystyle U = u \times A d = \frac{1}{2}\varepsilon_0 E^2 A d \)
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 – “… From Eqs. (2.70) and (2.71), we get Energy stored in the capacitor
\( \displaystyle U = \left(1/2\right)\varepsilon_0 E^2 \times A d \qquad (2.72) \)
Note that Ad is the volume of the region between the plates (where electric field alone exists).”