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The mean electric energy density between the plates of a charged capacitor is (where $q$ is the charge on the capacitor and $A$ is the area of the capacitor plate)

1. $\dfrac{q^2}{2\varepsilon_0 A^2}$
2. $\dfrac{q^2}{\varepsilon_0 A^2}$
3. $\dfrac{q^2}{2\varepsilon_0^2 A^2}$
4. None of the above

Correct answer: $\dfrac{q^2}{2\varepsilon_0 A^2}$

Solution

The electric field between the plates is $E=\frac{q}{\varepsilon_0 A}$. The mean energy density is $u=\frac{1}{2}\varepsilon_0 E^2$, so substituting gives $u=\frac{1}{2}\varepsilon_0\left(\frac{q}{\varepsilon_0 A}\right)^2=\frac{q^2}{2\varepsilon_0 A^2}$.

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