$A$ square surface of side $L \; m$ in the plane of the paper is placed in a uniform electric field $E \; (V/m)$ acting along the same plane at an angle $\theta$ with the horizontal side of the square as shown in the figure. The electric flux linked to the surface,in units of $V \cdot m$,is:

$A$ cubical Gaussian surface has a side of length $a = 10 \,cm$. Electric field lines are parallel to the $X$-axis as shown in the figure. The magnitudes of the electric fields through surfaces $ABCD$ and $EFGH$ are $6 \,kNC^{-1}$ and $9 \,kNC^{-1}$ respectively. Then,the total charge enclosed by the cube is (Take $\varepsilon_0 = 9 \times 10^{-12} \,Fm^{-1}$): (in $\,nC$)

Which statement$(s)$ among the following are incorrect:
$(i)$ $A$ negative test charge experiences a force opposite to the direction of the field.
$(ii)$ The tangent drawn to a line of force represents the direction of electric field.
$(iii)$ The electric field lines never intersect.
$(iv)$ The electric field lines form a closed loop.

$A$ circular plate sheet of radius $10 \,cm$ is placed in a uniform electric field of $2 \sqrt{3} \times 10^5 \,NC^{-1}$, making an angle of $60^{\circ}$ with the field. Find the electric flux through the sheet.

Three positive charges of equal value $q$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in:

The electric flux from a cube of edge $l$ is $\phi$ for an enclosed charge. If the edge of the cube is made $\frac{2}{3} l$ and the charge enclosed in the cube is doubled,then the electric flux value will be