Discussion
The electrostatic energy density of the electric field E in a capacitor is directly proportional to
Answer: A
The energy density is proportional to \(E^{2}\).
The energy stored per unit volume in an electric field is:
\[ u = \frac{1}{2}\varepsilon_{0}E^{2} \]
It follows from the capacitor energy \(\frac{1}{2}CV^{2}\) with \(C = \frac{\varepsilon_{0}A}{d}\) and \(V = Ed\), divided by the volume \(Ad\). Doubling the field quadruples the stored energy density.
\(E\), \(\sqrt{E}\) and \(E^{3}\) have the wrong power, and \(E^{-2}\) would make a stronger field store less energy.
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