An isolated conduction sphere sphere whose radius `R=1` m has a charge `q=1/9nC.` The energy density at the surfasce of the sphere is

Options

A. `(epsi_(0))/(2) J//m^(2)`
B. `epsi_(0)J//m^(2)`
C. `2epsi_(0) J//m^(3)`
D. `(epsi_(0))/(3) J//m^(3)`

Answer

A

Explanation

`E=q/(4 pi e_0 R^2)` and energy density `=1/2 e_0 e^2=1/2 e_0 q^2/(16 pi^2 e_0^2 R^4)`
`=e_0/2 (9 times 10^9)^2.(1/9 times 10^-9)^2 times (1)^(1/4)=e_0/2 J//m^3`