Consider an electric field  $\overrightarrow{\mathrm{E}}={\mathrm{E}}_0\hat{\mathrm{x}}$, where E₀ is a constant. The flux through the area (as shown in the figure) due to this field is :

$\text{Here, }\overrightarrow{\mathrm{E}}={\mathrm{E}}_0\widehat{\mathrm{x}}$
In this problem, $\hat{\mathrm{x}}, \hat{\mathrm{y}} \mathrm{and} \hat{\mathrm{z}}$ are the unit vectors along x, y and z axes respectively
Shaded area, $\overrightarrow{\mathrm{A}}=\overrightarrow{\mathrm{PQ}}\times \overrightarrow{\mathrm{QR}}$
$\begin{array}{l}\overrightarrow{\mathrm{A}}=(0\widehat{\mathrm{x}}+\mathrm{a}\widehat{\mathrm{y}}+0\widehat{\mathrm{z}})\times (\mathrm{a}\widehat{\mathrm{x}}+0\widehat{\mathrm{y}}+\mathrm{a}\widehat{\mathrm{z}})\\ \mathrm{\varphi }=\overrightarrow{\mathrm{E}}\cdot \overrightarrow{\mathrm{A}}=\left({\mathrm{E}}_0\widehat{\mathrm{x}}\right)\cdot \left({\mathrm{a}}^2\widehat{\mathrm{x}}-{\mathrm{a}}^2\widehat{\mathrm{z}}\right)={\mathrm{E}}_0{\mathrm{a}}^2\end{array}$