The electric field in a region is radially outward with magnitude `E=Agamma_(0)`. The charge contained in a sphere of radius `gamma_(0)` centered at the origin is

Options

A. `(1)/(4piepsi_(0))Ar_(0)^(3)`
B. `4piepsi_(0)Ar_(0)^(3)`
C. `(4piepsi_(0)A)/(r_(0))`
D. `(1)/(4piepsi_(0))(A)/(r_(0)^(3))`

Answer

B

Explanation

if Q is the charge enclosed by the sphere then the Gauss's law the fflux linked with the given sphere `phi=(Q)/(epsi_(0)) or Q=phiepsi_(0)`
but `phi=Eds=Ar_(0)xx4pir_(0)^(2)=4piAr_(0)^(3)(because E=Ar_(0))`
`therefore Q=phiepsi_(0)=4piepsi_(0)Ar_(0)^(3)`