The electric field in a region is radially out ward with magnitude E = Ar. Find the charge contained in a sphere of radius 20 cm. Given $\mathrm{A}=100{\mathrm{Vm}}^{-2}$.

Given data: $A=100{\mathrm{Vm}}^{-2}$, $\text{ a region's electric field radiates outward with magnitude }$E=A r

Concept used: electric field and electric field lines.

Detailed solution: 

$E=Ar\text{, Radius of sphere, }r=20 \mathrm{cm}=20\times {10}^{-2} \mathrm{m}$

 $A=100{\mathrm{Um}}^{-2}$ 

 $\text{ so, electric field due the sphere }=Ar$

 $=100\times 20\times {10}^{-2} N/\mathrm{C}$

 $=20 \mathrm{N}/\mathrm{C}$ 

 $\Rightarrow E.\left(4\pi r^2\right)=\frac{Q_{\text{inc }}}{{\epsilon }_0}$ 

$\Rightarrow Q_{\text{inc }}=\frac{20\times 20\times 20\times {10}^{-4}}{9\times {10}^9}$ 

 $=\frac{8}{9}\times {10}^{-10}\mathrm{C}$