Question

The cube shown in the figure has sides of length $L=10.0\text{cm}$. The electric field is uniform, has a magnitude $E=4.00\times {10}^{-3}{\text{NC}}^{-1}$ and is parallel to the $xy$ plane at an angle of ${37}^{\circ }$ measured from the $+x$-axis toward the $+y$-axis.
Given $\sin {37}^{\circ }=0.6$, $\cos {37}^{\circ }=0.8$



$\left(i\right)$ The surface(s) that have zero electric flux through them are

​​​​​​​$[$1 Mark$]$

• A. $S_1\text{and}{S}_3$
• B. $S_5\text{and}{S}_6$
• C. $S_2\text{and}{S}_4$
• D. $S_1\text{and}{S}_5$

Answer 1

The correct option is C $S_2\text{and}{S}_4$

Electric flux is given by
$\varphi =\overrightarrow{E}.\overrightarrow{A}=EA\cos \theta$
$\varphi$ will be $0$ when $\overrightarrow{E}$ and $\overrightarrow{A}$ are perpendicular.
The direction of area will be the direction perpendicular to the plane of area.

For surfaces $S_2$ and $S_4$ area vector $\overrightarrow{A}$ will be along $z$ - axis.

Since $\overrightarrow{E}$ is in $xy$ plane, for surfaces $S_2$ and $S_4$ area vector $\overrightarrow{A}$ will be perpendicular to the electric field

$\therefore \varphi$ for $S_2$ and $S_4$ will be zero.

So option $\left(c\right)$ is correct.