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.

$A$ line charge of length $\frac{a}{2}$ is kept at the center of an edge $BC$ of a cube $ABCDEFGH$ having edge length $a$ as shown in the figure. If the linear charge density is $\lambda \; C/m$, then the total electric flux through all the faces of the cube will be . . . . . . . (Take $\varepsilon_0$ as the free space permittivity)

If some charge is given to a solid metallic sphere,the field inside remains zero and by Gauss's law all the charge resides on the surface. Now,suppose that Coulomb's force between two charges varies as $1 / r^{3}$. Then,for a charged solid metallic sphere

An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell,as shown in the figure. The permittivity of free space is $\epsilon_0$. Which of the following statements is (are) true?
$(A)$ The electric flux through the shell is $\sqrt{3} R \lambda / \epsilon_0$
$(B)$ The $z$-component of the electric field is zero at all the points on the surface of the shell
$(C)$ The electric flux through the shell is $\sqrt{2} R \lambda / \epsilon_0$
$(D)$ The electric field is normal to the surface of the shell at all points

Four closed surfaces and corresponding charge distributions are shown below. Let the respective electric fluxes through the surfaces be $\phi_1, \phi_2, \phi_3$ and $\phi_4$. Then:

$A$ 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 . . . . . . .