Charges are placed on the vertices of a square as shown in the figure. Let $\vec{E}$ be the electric field and $V$ be the electric potential at the center. If the charges at $A$ and $B$ are interchanged with those at $D$ and $C$ respectively,then:

The figure shows a nonconducting ring which has positive and negative charge non-uniformly distributed on it such that the total charge is zero. Which of the following statements is true?

$A$ charge $q$ is placed in the middle of a line joining two equal and like point charges $Q$. For what value of $q$ will the system be in equilibrium?

Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of a $(X, Y)$ coordinate system. Then:

Two electric charges $+2 \mu C$ and $-4 \mu C$ are separated by a distance $3 \ m$ in air. At a point $P$ located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field at point $P$ (in $NC^{-1}$) is (in $,000$)

$A$ 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: