Question

An isolated conducting sphere whose radius $R=1m$ has a charge $q=\frac{1}{9}$ $nC$. The energy density at the surface of the sphere is :

• A. $\frac{{\epsilon }_0}{2}J/m^3$
• B. ${\epsilon }_{0}J/m^3$
• C. $2{\epsilon }_{0}J/m^3$
• D. $\frac{{\epsilon }_0}{3}J/m^3$

Answer 1

The correct option is A $\frac{{\epsilon }_0}{2}J/m^3$

Energy density , $u=\frac{1}{2}{ϵ}_0{E}^2$

here, the electric field at the surface of sphere is $E=\frac{1}{4\pi {ϵ}_0}\frac{q}{R^2}=9\times {10}^9\times \frac{1/9\times {10}^{-9}}{1^2}=1N/C$

Thus, $u=\frac{1}{2}{ϵ}_{0}J/m^3$