The electric field in a region is radially outward with magnitude `E=Ar`. Find the charge contained in a sphere of radius a centred at the origin. Take `A=100 V m^(-2)` and `a=20.0 cm`.

Explanation

Given `E=alphar`, when `r=R`
`ER=alphaR`
So `phi=E_(R)("area")=alphaR4piR^(2)`
by gauss's theorem the net electric flux is
`(1)/(epsilon_(0))` charged enclosed
`alphaR4piR^(2)=(1)/(epsilon_(0))Q_("enclosed")`
`thereforeQ_("enclosed")=(4piepsilon_(0))alphaR^(3)`
Given `R=0.30m,alpha=100Vm^(-2)`
`Q_("enclosed")=(1)/(9xx10^(9))xx100xx(0.30)^(3)=3xx10^(-10)C`