The electric field in a region is radially outward with magnitude E=αr. If α=100Vm−2 and R=0.30m then the value of charge contained in a sphere of radius R centered at the origin is W×10−10C.Find W.

Given E=αr. When r=R,ER=αR.  So ϕ=ER(area )=αR4πR2By Gauss's theorem, the net electric flux is1ε0 charge enclosed αR4πR2=1ε0Qenclosed ∴ Qenclosed =4πε0αR3Given R=0.30m,α=100Vm−2Qenclosed =19×109×100×(0.30)3=3×10−10C