The electric field in a region is given by $\overrightarrow{E} = \frac{2}{5} E_{0} \hat{i} + \frac{3}{5} E_{0} \hat{j}$ with $E_{0} = 4.0 \times 10^{3} \, N/C$. The flux of this field through a rectangular surface area $0.4 \, m^{2}$ parallel to the $Y-Z$ plane is ....... $N m^{2} C^{-1}$.

Which among the curves shown in the figure cannot possibly represent electrostatic field lines?

$A$ rectangular surface of sides $10 \,cm$ and $15 \,cm$ is placed inside a uniform electric field of $25 \,V/m$,such that the surface makes an angle of $30^{\circ}$ with the direction of the electric field. Find the flux of the electric field through the rectangular surface in $Nm^2/C$.

Consider four closed surfaces $S_1, S_2, S_3,$ and $S_4$ each enclosing the same charge $q_1$. Compare the electric flux through these surfaces.

$A$ square loop of sides $a=1 \ m$ is held normally in front of a point charge $q=1 \ C$. The charge is placed at a distance of $a/2$ from the center of the square. The flux of the electric field through the shaded region is $\frac{5}{p} \times \frac{1}{\varepsilon_0} \frac{N m^2}{C}$,where the value of $p$ is . . . . . . .

The electric field in a region of space is given by $\vec{E} = (5\hat{i} + 2\hat{j}) \text{ N/C}$. Calculate the electric flux through a surface of area $2 \text{ m}^2$ lying in the $YZ$-plane.