The electric field in a region is radially outward with magnitude `E = ar`. If `a = 100 Vm^(-2)` and `R = 0.30m`, then the value of charge contained in a sphere of radius R centred at the origin is `W xx 10^(-10)C`. Find W.

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`