Question

A large conducting plane has surface charge density ${10}^{-2}C/m^2$. Find the electrostatic energy stored in a cubical volume of side $1cm$ in the front plane.

• A. $1.4J$
• B. $2.8J$
• C. $5.6J$
• D. none of these

Answer 1

The correct option is C $5.6J$

The electric field due to the conducting plane near cube is $E=\frac{\sigma }{{ϵ}_0}$
The energy stored in cube is $U=\frac{{ϵ}_0}{2}\int E^{2}d\tau =\frac{{\sigma }^2}{2{ϵ}_0}\int d\tau =\frac{{\sigma }^2}{2{ϵ}_0}\times \left(Volumeofcube\right)$
or $U=\frac{{10}^{-4}}{2\times 8.85\times {10}^{-12}}\times {10}^{-6}=5.6J$