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

Given E=αr.  When  r=R,  E=αR.  So  ϕ=ER(area)=αR4πR2 By Gauss's theorem, the net electric flux is1ε0 charge enclosedαR4πR2=1ε0Qenclosed∴Qenclosed=(4πε0)αR3Given R=0.30 m,α=100  Vm−2Qenclosed=19×109×100×(0.30)3=3×10−10 C