$A$ total charge $q$ is divided into $q_1$ and $q_2$,which are placed at two vertices of an equilateral triangle of side $a$. The magnitude of the electric field $E$ at the third vertex of the triangle is to be depicted schematically as a function of $x = q_1 / q$. Choose the correct figure.

The following figures show regular hexagons with charges placed at their vertices. In which of the following cases is the electric field at the center zero?

Two equal negative charges are fixed at the points $(0, a)$ and $(0, -a)$ on the $y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $x$-axis. The charge $Q$ will

Given below are two statements:
Statement-$I$: $A$ point charge is brought into an electric field. The value of the electric field at a point near the charge may increase if the charge is positive.
Statement-$II$: An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.
Choose the correct answer from the options given below:

$A$ tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81 \pi}{7} \times 10^5 \text{ Vm}^{-1}$. When the field is switched off,the drop is observed to fall with a terminal velocity $2 \times 10^{-3} \text{ ms}^{-1}$. Given $g = 9.8 \text{ ms}^{-2}$,viscosity of the air $\eta = 1.8 \times 10^{-5} \text{ Ns m}^{-2}$,and the density of oil $\rho = 900 \text{ kg m}^{-3}$,the magnitude of $q$ is:

Two charged identical metal spheres $A$ and $B$ repel each other with a force of $3 \times 10^{-5} \,N$. Another identical uncharged sphere $C$ is touched with sphere $A$ and then it is placed mid-way between $A$ and $B$. Then, the magnitude of net force on $C$ is