The electric flux through the surface shown in FIGURE EX24.11 is $25N{m}^2/C$. What is the electric field strength?

Given :

Electric flux through the surface :$25N{m}^2/C$

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.

${\Phi }_e=E·A·\cos \theta$ (1)

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 :

$\theta =90°-30°=60°$

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

role="math" localid="1649658814933" $A=(0.10m\times 0.20m)=2x{10}^{-2}m²$

Rewriting equation (1), we get :

$E=\frac{{\Phi }_e}{A\cos \theta }$ (2)

Plugging in our values for $E,A\mathrm{and}\theta$into equation (2) to get the electric flux :

$$\begin{gathered} E=\frac{{\Phi }_e}{A\cos \theta } \\ =\frac{(25N·m²/C}{(2x{10}^{-2}m²)(\cos 30°)} \\ =\boxed{\mathbf{1}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{}\mathbf{N}\mathbf{/}\mathbf{C}} \end{gathered}$$