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A parallel plate condenser has a uniform electric field E (V/m) in the space between the plates. If the distance between the plates is d (m) and area of each plate is A ($m^2$), the energy (joules) stored in the condenser is
A
$\frac{1}{2}\varepsilon_0E^2Ad$
B
$E^2Ad/\varepsilon_0$
C
$\frac{1}{2}\varepsilon_0E^2$
D
$\varepsilon_0EAd$
Detailed Solution
Energy stored per unit volume in an electric field (energy density): $u = \frac{1}{2}\varepsilon_0E^2$
The field is uniform and confined to the space between the plates, whose volume = Ad.
Energy stored = energy density × volume
$U = \frac{1}{2}\varepsilon_0E^2\times Ad$
Check: $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{\varepsilon_0A}{d}(Ed)^2 = \frac{1}{2}\varepsilon_0E^2Ad$
The field is uniform and confined to the space between the plates, whose volume = Ad.
Energy stored = energy density × volume
$U = \frac{1}{2}\varepsilon_0E^2\times Ad$
Check: $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{\varepsilon_0A}{d}(Ed)^2 = \frac{1}{2}\varepsilon_0E^2Ad$