What is the electric flux through the surface shown in FIGURE EX24.9?

Given figure :

Theory used :

The quantity of electric field passing through a closed surface is known as the Electric flux. Gauss's law indicates that the electric field across a surface is proportional to the angle at which it passes, hence we can determine charge inside the surface using the equation below.

${\Phi }_e=E·A·\cos \theta$

Where $\theta$is the angle formed between the electric field and the normal.

The electric field is uniform here, and the sheet is tilted to the electric field by an angle of $30°$, hence we use equation (1) to calculate flux.

As indicated in the diagram, $\theta$may be calculated as :

$\theta =90°+30°=120°$

On the flat sheet, where $\theta$does not change and $A$is the area of the flat sheet, which we can get by :

$A=(0.15m\times 0.15m)=2.25x{10}^{-2}m²$

Plugging in our values for $E,A\mathrm{and}\theta$into equation (1) to get the electric flux :

$$\begin{gathered} {\Phi }_e=EA\cos \theta \\ =(180N/C)(2.25x{10}^{-2}m²)(\cos 120°) \\ =\boxed{\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{3}\mathbf{}\mathit{N}\mathbf{·}\mathit{m}\mathbf{²}\mathbf{/}\mathit{C}} \end{gathered}$$