(C) The potential difference $V$ between the plates of a parallel plate capacitor in a uniform electric field $E$ is given by $V = Ed$.The capacitance

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$\frac{1}{2} \varepsilon_0 E^2 Ad$

(C) The potential difference $V$ between the plates of a parallel plate capacitor in a uniform electric field $E$ is given by $V = Ed$.The capacitance $C$ of a parallel plate capacitor is given by $C = \frac{\varepsilon_0 A}{d}$.The energy $U$ stored in a capacitor is given by the formula $U = \frac{1}{2} CV^2$.Substituting the expressions for $C$ and $V$ into the energy formula:$U = \frac{1}{2} \left( \frac{\varepsilon_0 A}{d} \right) (Ed)^2$$U = \frac{1}{2} \left( \frac{\varepsilon_0 A}{d} \right) E^2 d^2$$U = \frac{1}{2} \varepsilon_0 E^2 Ad$.

Class 12 Physics Electric Potential and Capacitance Energy Stored in a Capacitor

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$A$ 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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A
$\varepsilon_0 EAd$
B
$\frac{1}{2} \varepsilon_0 \frac{E^2}{Ad}$
C
$\frac{1}{2} \varepsilon_0 E^2 Ad$
D
$\varepsilon_0 \frac{E^2}{Ad}$

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Electric Potential and Capacitance

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Energy Stored in a Capacitor

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$A$ 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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$A$ $10 \, pF$ capacitor is connected to a $50 \, V$ battery. How much electrostatic energy is stored in the capacitor?

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