Question

The mean electric energy density between plates of a charged capacitor:

• A. $\frac{q^2}{2E_o{A}^2}$
• B. $\frac{q}{2E_o{A}^2}$
• C. $\frac{q^2}{2E_{o}A}$
• D. None of the above

Answer 1

Answer: (A)

Electric energy stored in capacitor
$U=\frac{1}{2}\frac{q}{C}=\frac{1}{2}\frac{q^2}{{\epsilon }_{0}A/d}$
multiply and divide by A
$=\frac{1}{2}\frac{q^2}{{\epsilon }_0{A}^2}\times A\times d=\frac{q^{2}d}{2{\epsilon }_{0}A}$
$\therefore$ Mean electric energy density between the plates of charged capacitor
$\frac{U}{Ad}=\frac{1}{2}\frac{q^2}{{\epsilon }_0{A}^2}$