Question

Consider an electric field $E=E_0\, \hat{x},$ Where $E_0$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is

• A. $2 E_0 a^2$
• B. $ \sqrt 2 E_0 a^2$
• C. $ E_0 a^2$
• D. $\frac{E_0 a^2}{\sqrt2}$

Answer 1

Answer: (C)

Electric flux, $\varnothing = E.S$ or $\varnothing = ES\, \cos \theta$
Here, $\theta$ is the angle between $E$ and $S$.
In this question $\theta = 45^{\circ},$ because S is perpendicular to surface.
$E = E_0$
$S = (\sqrt 2 a) (a) = \sqrt 2 a^2$
$\therefore \theta =(E_0) (\sqrt 2 a^2)\cos\, 45^{\circ} = E_0 a^2$