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Question

(A) The energy density $u$ (energy per unit volume) in a region with an electric field $E$ is given by the formula: $u = \frac{1}{2} \varepsilon_{0} E

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$\frac{1}{2} \varepsilon_{0} E^{2} Ad$

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(A) The energy density $u$ (energy per unit volume) in a region with an electric field $E$ is given by the formula: $u = \frac{1}{2} \varepsilon_{0} E^{2}$.The volume $V$ of the space between the plates of the capacitor is the product of the area $A$ and the distance $d$,so $V = Ad$.The total energy $U$ stored in the capacitor is the product of the energy density and the volume:$U = u 	imes V$$U = (\frac{1}{2} \varepsilon_{0} E^{2}) 	imes (Ad)$$U = \frac{1}{2} \varepsilon_{0} E^{2} Ad$.

$A$ parallel plate capacitor has a uniform electric field $E$ 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:

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