Question

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

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

Answer 1

Answer: (A)

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