The energy required to charge a parallel plat | vedclass

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(D) The energy stored in a parallel plate capacitor is given by the formula $U = \frac{1}{2} C V^{2}$.Here,the capacitance $C = \frac{\varepsilon_{0}

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$\frac{1}{2} \varepsilon_{0} E^{2} A d$

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(D) The energy stored in a parallel plate capacitor is given by the formula $U = \frac{1}{2} C V^{2}$.Here,the capacitance $C = \frac{\varepsilon_{0} A}{d}$.The potential difference $V$ between the plates is related to the electric field $E$ and separation $d$ by $V = E d$.Substituting these values into the energy formula:$U = \frac{1}{2} \left( \frac{\varepsilon_{0} A}{d} \right) (E d)^{2}$$U = \frac{1}{2} \left( \frac{\varepsilon_{0} A}{d} \right) (E^{2} d^{2})$$U = \frac{1}{2} \varepsilon_{0} E^{2} A d$.

The energy required to charge a parallel plate capacitor with plate separation $d$ and plate area $A$ such that the uniform electric field between the plates is $E$,is

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