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Question

(C) The energy density $(u)$ of an electric field in free space is given by the formula: $u = \frac{1}{2}\epsilon_0E^2$. The volume $(V)$ of the space

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$\frac{1}{2}A\epsilon_0E^2d$

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(C) The energy density $(u)$ of an electric field in free space is given by the formula: $u = \frac{1}{2}\epsilon_0E^2$. The volume $(V)$ of the space between the plates of the capacitor is the product of the area of the plates $(A)$ and the distance between them $(d)$, so $V = A \cdot d$. The total energy $(U)$ stored in the capacitor is the product of the energy density and the volume: $U = u \cdot V$. Substituting the expressions, we get: $U = (\frac{1}{2}\epsilon_0E^2) \cdot (A \cdot d)$. Therefore, the energy stored is $U = \frac{1}{2}A\epsilon_0E^2d$.

$A$ parallel plate air capacitor having area of each plate $A$ and the distance between the plates $d$ has a uniform electric field $E$ in the space between the plates. The energy stored in the capacitor is ($\epsilon_0$ = permittivity of free space).

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