Question: 21. A parallel plate capacitor has a uniform electric field ‘ \vec{E} ‘ in the space between the plates. If the distance between the plates is ‘ d ‘ and the area of each plate is ‘A’, the energy stored in the capacitor is: ( \varepsilon_{0}= permittivity of free space)
(1) \frac{1}{2} \varepsilon_{0} \mathrm{E}^{2}
(2) \varepsilon_{0} \mathrm{EAd}
(3) \frac{1}{2} \varepsilon_{0} \mathrm{E}^{2} \mathrm{Ad}
(4) \frac{\mathrm{E}^{2} \mathrm{Ad}}{\varepsilon_{0}}
Answer: Option (3)
Explanation:
The energy density stored in an electric field is given by u=\frac{1}{2}\varepsilon_{0}E^{2}.
The total energy stored in the capacitor is equal to the energy density multiplied
by the volume between the plates.
The volume between the plates is V=Ad.
Therefore, the total energy stored is U=u \times V.
Substituting the values, U=\frac{1}{2}\varepsilon_{0}E^{2}\times Ad.
This gives U=\frac{1}{2}\varepsilon_{0}E^{2}Ad.
Hence, the correct answer is Option (3).