First slide

Electric Flux

Question

Consider an electric field $\vec{E} = E_{0} \hat{x}$ , where E₀ is a constant. The flux through the area (as shown in the figure) due to this field is :

Difficult

A

2E₀a²
B

$\sqrt{2}$ E₀a²
C

E₀a²
D

$\frac{2 E_{0} a^{2}}{\sqrt{2}}$

Solution

$Here, \vec{E} = E_{0} \hat{x}$
In this problem, $\hat{x}, \hat{y} and \hat{z}$ are the unit vectors along x, y and z axes respectively
Shaded area, $\vec{A} = \vec{PQ} \times \vec{QR}$
$\begin{array}{l} \vec{A} = (0 \hat{x} + a \hat{y} + 0 \hat{z}) \times (a \hat{x} + 0 \hat{y} + a \hat{z}) \\ ϕ = \vec{E} \cdot \vec{A} = (E_{0} \hat{x}) \cdot (a^{2} \hat{x} - a^{2} \hat{z}) = E_{0} a^{2} \end{array}$

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