Question

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

Answer 1

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

$A=100{Um}^{-2}$

So, electric field due the sphere $=Ar$

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

$=20N/C$

Now, Using gauss law, which states that for a sphere of radius $r$.

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

or $E\left(4\pi {\epsilon }_0\right)\left(r^2\right)=Q_{inc}$

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

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