Question

The electric field in a region is $E=\frac{5\times {10}^{3}x}{2}\hat{i}N{C}^{-1}c{m}^{-1}$. The charge contained inside a cubical volume bounded by the surfaces $x=0,x=1,y=0,y=1,z=0,z=1$ is (where x, y, z are in cm) :

• A. $2.21\times {10}^{-12}C$
• B. $4.42\times {10}^{-12}C$
• C. $2.21\times {10}^{-8}C$
• D. $4.42\times {10}^{-8}C$

Answer 1

The correct option is A $2.21\times {10}^{-12}C$

Area of each surfaces $a=1^{2}c{m}^2={10}^{-4}{m}^2$.
As the field is in the direction of x-axis so only surfaces $x=0$ and $x=1$ will contribute the flux.
For surface $x=0,{\varphi }_0=E.a=\frac{5\times {10}^3\times x}{2}.a=\frac{5\times {10}^3\times 0}{2}.a=0$
and for $x=1,{\varphi }_1=E.a=\frac{5\times {10}^3\times x}{2}.a=\frac{5\times {10}^3\times 1}{2}\times {10}^{-4}=0.25$
By Gauss's law, ${\varphi }_1=\frac{q_{en}}{{ϵ}_0}$
$\Rightarrow q_{en}=0.25\times 8.85\times {10}^{-12}=2.21\times {10}^{-12}C$