Question

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

Short answer

The electric flux through the surface is$\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{3}\mathbf{}\mathit{N}\mathbf{·}\mathit{m}\mathbf{²}\mathbf{/}\mathit{C}$

Step-by-step solution

Given information and Theory used

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.

Calculating the electric flux

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 :

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