91影视

1. Length of each edge of the cube is $\mathrm{a}=3.0\mathrm{m}$
2. The field at the top face of the cube is role="math" localid="1657341831037" $\stackrel{鈫�}{\mathrm{E}}=-34\hat{\mathrm{k}}\mathrm{N}/\mathrm{C}$, and at the bottom face it is role="math" localid="1657341820720" $\stackrel{鈫�}{\mathrm{E}}=+20\hat{\mathrm{k}}\mathrm{N}/\mathrm{C}$

The net flux through each cube surface is given by dividing the total flux value through the cube by 6. Thus, the net flux is given using the concept of the Gauss flux theorem.

Formula:

The enclosed charge within the surface,

${\mathrm{q}}_{\mathrm{enc}}={\mathrm{蔚}}_0\mathrm{蠒}={\mathrm{蔚}}_0(\mathrm{E}.\mathrm{A})$ (1)

There is no flux through the sides, so we have two 鈥渋nward鈥� contributions to the flux, one from the top (of magnitude$\left(34\right){\left(3.0\right)}^2$) and one from the bottom (of magnitude$\left(20\right){\left(3.0\right)}^2$). With 鈥渋nward鈥� flux being negative, the result of the net flux is given using equation (1) such that,

role="math" localid="1657342360739" $\begin{array}{l}\mathrm{蠒}=-\left((34\mathrm{N}/\mathrm{C}){(3.0\mathrm{m})}^2+(20\mathrm{N}/\mathrm{C}){(3.0\mathrm{m})}^2\right)\\ =-486\mathrm{N}.{\mathrm{m}}^2/\mathrm{C}\end{array}$.

Now, the net charge enclosed within the surface is given using equation (1) such that,

$$\begin{gathered} {\mathrm{q}}_{\mathrm{enc}}=\left(8.85\mathrm{x}{10}^{-12}{\mathrm{C}}^2/\mathrm{N}.{\mathrm{m}}^2\right)(-486\mathrm{N}.{\mathrm{m}}^2/\mathrm{C}) \\ =-4.3脳{10}^{-9}\mathrm{C} \end{gathered}$$

Hence, the value of the charge is $-4.3脳{10}^{-9}\mathrm{C}$.