• # question_answer The electric field in a region is radially outward with magnitude$E=Ar$. The charge contained in a sphere of radius${{r}_{0}}$centered at the origin is A)  $\frac{1}{4\pi {{\varepsilon }_{0}}}Ar_{0}^{3}$ B)  $4\pi {{\varepsilon }_{0}}\,Ar_{0}^{3}$ C)  $\frac{4\pi {{\varepsilon }_{0}}A}{r_{0}^{3}}$ D)  $\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{A}{r_{0}^{3}}$

: Intensity [E] at surface of sphere$=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{r_{0}^{2}}$ Since$E=A{{r}_{0}}$ $\therefore$ $A{{r}_{0}}=\frac{Q}{4\pi {{\varepsilon }_{0}}r_{0}^{2}}$ or  $Q=4\pi {{\varepsilon }_{0}}Ar_{0}^{3}$