Question

The volume charge density as a function of distance x from one face inside a cube of side 2 m, is varying as shown in the figure. Find the total flux (in S.I. units) through the cube. (If ${\rho }_0=8.85\times {10}^{-12}C/m^3$) ___

Answer 1

Charge inside cube $=\left(Areaofgraph\right)\times (side{)}^2$
$Q=({\rho }_0\times \frac{3}{2})\times (2{)}^2$
$=6{\rho }_0$
$Flux,\varphi =\frac{Q}{{\epsilon }_0}=\frac{6{\rho }_0}{{\epsilon }_0}$
$=\frac{6\times 8.85\times {10}^{-12}}{8.85\times 106-12}=6$