A thin spherical shell encloses a concentric solid sphere. The radius of the shell is `(0.060)^((1)/(2))`m and its surface charge density is `-10^(-6)C//m^(2)`. The radius of the solid sphere is `(0.01)^((1)/(3))m` and its volumetric charge density is `3 xx 10^(-5)C//m^(3). epsi_(0)` is the permittivity of free space in `C^(2)//Nm^(2)`. The electric flux through a spherical surface concentric with the spherical shell and of radius greater than that of the shell in V-m is

Options

A. `(0.4 pi xx 10^(-7))/(epsi_(0))`
B. `(0.8 pi xx 10^(-7))/(epsi_(0))`
C. `(1.2 pi xx 10^(-7))/(epsi_(0))`
D. `(1.6 pi xx 10^(-7))/(epsi_(0))`

Answer

D

Explanation

Electric flux through spherical surface
`(q_("net enclosed"))/(epsi_(0)) = ("Charge of shell + Charge of sphere")/(epsi_(0))`
`= (1)/(epsi_(0)) `[(4pi (0.06)^((1)/(2)) x(-10)^(-6)),(+ (4)/(3) pi (0.01^((1)/(3)))^(3) xx 10^(-5))]`
`=(pi)/(epsi_(0)) {-0.24 xx 10^(-6) + 0.39 xx 10^(-6)}`
`= (1.6 pi xx 10^(-7))/(epsi_(0)) V-m`