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^3`
B. `epsilon_0 Aa^3`
C. `4piepsilon_0Aa^2`
D. `Aepsilon_0a^2`

Answer

A

Explanation

`oint vecE.vec(dS)=Q_"in"/epsilon_0`
`vecE.vecS=Q_"in"/epsilon_0`
`F,4pia^2=Q_"in"/epsilon_0`
`Aa.4pia^2 = Q_"in"/epsilon_0`
`Q_"in"=4piepsilon_0Aa^3`