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

$(a)\;\large\frac{\in_{0}}{2}\;J/m^3\qquad(b)\;\in\;J/m^3\qquad(c)\;2 \in_{0} \;J/m^3\qquad(d)\;\large\frac{\in_{0}}{3}\;J/m^3$

Answer : (a ) $\;\large\frac{\in_{0}}{2}\;J/m^3$
Explanation :
Energy density = $\;\large\frac{1}{2}\;\in_{0}|E|^2$
$=\large\frac{1}{2}\in_{0}\;(\large\frac{k\;q}{R^2})^2$
$=\large\frac{1}{2}\in_{0}\;(9\times10^9\times\large\frac{1}{9}\times10^{-9})\times1$
$=\large\frac{\in_{0}}{2}\;.$