Consider an electric field $\vec{E} = 3 \times 10^3 \hat{i} \text{ N/C}$. What is the flux through a square of side $10 \text{ cm}$ in $Nm^2/C$ if the normal to its plane makes a $60^\circ$ angle with the $X$-axis?

Choose the correct option based on the given electric field lines diagram.

The net electric flux due to a uniform electric field of $3 \times 10^3 \hat{i} \text{ NC}^{-1}$ through a cube of side $20 \text{ cm}$ oriented such that its faces are parallel to the coordinate planes is

Let the electrostatic field $E$ at distance $r$ from a point charge $q$ not be an inverse square but instead an inverse cubic, e.g., $E = k \cdot \frac{q}{r^3} \hat{r}$, where $k$ is a constant.
Consider the following two statements:
$(I)$ Flux through a spherical surface enclosing the charge is $\phi = q_{\text{enclosed}} / \varepsilon_0$.
$(II)$ $A$ charge placed inside a uniformly charged shell will experience a force.
Which of the above statements are valid?

An electric dipole is placed in the north-south direction inside a sphere filled with water. Which statement is correct?

$A$ charge of $20 \ \mu C$ is placed inside a closed surface. If an additional charge of $80 \ \mu C$ is placed inside the surface,the change in flux is: