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

Answer

c

Explanation

Let charge enclosed in the sphere of radius is `q` According to Gauss theorem,
`ointvec(E ).vec(d)s=(q)/(epsilon_(0))implies E.4pir^(2)=(q)/(epsilon_(0))`
We are given `E= Ar`, substituting this value in the above equation we get `4piAr^(3)=(q)/(epsilon_(0))` (i)
If `r=a`, then substituting the value in equation (i), we get `q= 4pi epsilon_(0)Aa^(3)`