Question

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

• A. $\frac{q^{2}}{2 \varepsilon_{0} A^{2}}$
• B. $\frac{q}{2 \varepsilon_{0} A^{2}}$
• C. $\frac{q^{2}}{2 \varepsilon_{0} A}$
• D. None of the above

Answer 1

Answer: (A)

Energy density
$=\frac{1}{2} \varepsilon_{0} E^{2}=\frac{1}{2} \varepsilon_{0}\left(\frac{\sigma}{\varepsilon_{0}}\right)^{2}$
$=\frac{\sigma^{2}}{2 \varepsilon_{0}}=\frac{q^{2}}{2 \varepsilon_{0} A^{2}}$