Question

The energy stored in a parallel plate capacitor of cross section area $A$ with a separation $d$ being filled with dielectric of dielectric constant $\varepsilon_{0}$ in terms of the electric field between them, $E$ is

• A. $\frac{1}{2} \varepsilon_{0} E^{2}$
• B. $\frac{1}{2} \varepsilon_{0} E^{2}\,Ad$
• C. $\frac{1}{2} \varepsilon_{0} E^{2}\,A/d$
• D. $\frac{1}{2} \varepsilon_{0} E^{2}d /A$

Answer 1

Answer: (B)

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

Answer 2

The capacitance of a parallel plate capacitor is $C=\frac{\varepsilon_{0} A}{d}$ The electric field between the plates is $E=\frac{V}{d}$ The energy stored in the capacitor is $U=\frac{1}{2}CV^{2}$ $=\frac{1}{2}\left(\frac{\varepsilon_{0} A}{d}\right)\left(Ed\right)^{2}$ $=\frac{1}{2} \varepsilon_{0}E^{2}Ad$