$A$ sphere of radius $R$ and charge $Q$ is placed inside an imaginary sphere of radius $2R$ whose center coincides with the given sphere. The flux related to the imaginary sphere is

The figure shows the electric field lines for a system of two charges. Choose the correct option regarding the electric field intensity at points $A$,$B$,and $C$.

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

An electric field is given by $\vec{E} = (6 \hat{i} + 5 \hat{j} + 3 \hat{k}) \ N/C$. The electric flux through a surface area $\vec{A} = 30 \hat{i} \ m^2$ (in $SI$ units) is:

Consider a uniform electric field $E = 3 \times 10^{3} \hat{i} \; N/C$.
$(a)$ What is the flux of this field through a square of $10 \; cm$ on a side whose plane is parallel to the $yz$ plane?
$(b)$ What is the flux through the same square if the normal to its plane makes a $60^{\circ}$ angle with the $x$-axis?

$A$ hemisphere of radius $R$ is placed in a uniform electric field $E$ so that its axis is parallel to the field. Which of the following statement$(s)$ is/are true?