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. `4pi epsilon_(0)A a^(3)`
B. `epsilon_(0)Aa^(3)`
C. `4pi epsilon_(0)Aa^(2)`
D. `A epsilon_(0) a^(2)`

Answer

A

Explanation

According to question, electric field varies as E = Ar
Here r is the radial distance.

At r = a, E = Aa …(i)
Net flux emitted from a spherical surface of radius a is
`phi_("net") = (q_("en"))/(epsilon_(0))`
`rArr (A a) xx (4pi a^(2)) = (q)/(epsilon_(0))` [Using equation (i)]
`:. q = 4pi epsilon_(0)A a^(3)`