Question

The electric flux density vector of a certain charge distribution is represented by $\overrightarrow{D}=12xyz\widehat{a_x}+(6x^{2}z+6yz)\widehat{a_y}+(6x^{2}y+3y^2)\widehat{a_z}C/m^2$

The amount of charge enclosed in cube having a volume of volume of ${10}^{-5}{m}^3$ located at (x=1 m,y = 1 m,z = 1 m) is _______$\mu C$.

• A. 180

Answer 1

The correct option is A 180
By Maxwell equation

$\nabla .\overrightarrow{D}={\rho }_v=\frac{\partial }{\partial x}\left(12xyz\right)+\frac{\partial }{\partial y}(6x^{2}z+6yz)+\frac{\partial }{\partial z}(6x^{2}y+3y^2)$

= 12yz + 6z
At point (1, 1, 1), $\nabla .\overrightarrow{D}=12+6=18C/m^2$

$Q=\int {\rho }_{v}dV=18\times {10}^{-5}=180\mu C$