The electric field in a region is given by $\;\overrightarrow{E}=\large\frac{\in_{0} x \hat{i}}{l}\;.$ Find the charge contained inside a cubical volume bounded by the surfaces $\;x=0 , x=a , y=0 , y=a , z=0 , z=a $ where $a= 10^{-2} m$ and $l= 2 \times 10^{-2}\; m$

Question

$(a)\;22\times10^{-12}\;C\qquad(b)\;0.22\times10^{-12}\;C\qquad(c)\;2.2\times10^{-12}\;C\qquad(d)\;4.4\times10^{-12}\;C$

Answer 1

Answer : (c) $\;2.2\times10^{-12}\;C$

Explanation : Electric flux through five surfaces is zero . The electric flux through on surface x=a plane is :

$\phi=\large\frac{\in_{0}\;a}{l}\;a^2=\large\frac{Q}{\in_{0}}$

$Q=\large\frac{\in_{0}\;a^3\;\in_{0}}{l}$

$Q=\large\frac{5\times10^3\times10^{-6}\times8.86\times10^{-12}}{2\times10^{-2}}$

$Q=2.2\times10^{-12}\;.$