The electric field in a certain region is acting radially outwards and is given by `E=Ar. A` charge contained in a sphere of radius `'a'` centred at the origin of the field, will given by

Options

A. `(1)/(4piepsilon_(0))Agamma_(0)^(3)`
B. `4pi epsilon_(0)Agamma_(0)^(3)`
C. `(4pi epsilon_(0)A)/(gamma_(0))`
D. `(1)/(4pi epsilon_(0))(A)/(gamma_(0)^(3))`

Answer

b

Explanation

Flux linked with the given sphere `varphi=(Q)/(epsilon_(0))`,
where `Q=` Charge enclosed by the sphere.
Hence `Q = phi epsilon_(0)=(EA)epsilon_(0)`
`implies Q=4pi(gamma_(0))^(2)xxAgamma_(0)epsilon_(0)=4pi epsilon_(0)A gamma_(0)^(3)`.