Chapter 6, Problem 6.1CYU

Check Your Understanding What angle should there be between the electric field and the surface show in Figure 6.11 in the previous example so that no electric flux passes through the surface?

To determine

The angle between the electric field and the surface for no flux passage through the surface.

Answer to Problem 6.1CYU

The angle between the electric field and the surface for no flux passage through the surface is $90°$ or $270°$.

Explanation of Solution

Formula used:

The electric flux passing through the surface is given by

  $\Phi =EA\cos \theta$

Here, $E$ is the electric field, $A$ is the surface area and $\theta$ is the angle between electric field and the surface.

Calculation:

The angle between electric field and the surfacefor no flux passage is calculated as follows:

  $\begin{array}{c}\theta ={\cos }^{-1}\left(\frac{\Phi }{EA}\right)\\ ={\cos }^{-1}\left(\frac{0}{EA}\right)\\ ={\cos }^{-1}\left(0\right)\\ =90°,270°\end{array}$

Conclusion:

The angle between the electric field and the surface for no flux passage through the surface is $90°$ or $270°$.