Two positive point charges of unequal magnitude are placed at a certain distance apart. $A$ small positive test charge $q$ is placed at the null point $N$. Then,

$A$ cube of a metal is given a positive charge $Q$. For the above system,which of the following statements is true?

Two charges,each equal to $\eta q$ (where $\eta^{-1} < \sqrt{3}$),are placed at two corners of an equilateral triangle of side $a$. The electric field at the third corner is $E_3$. If $E_0 = \frac{q}{4\pi\varepsilon_0 a^2}$,then which of the following is correct?

Two equal positive charges $q$ 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:

$(a)$ Consider an arbitrary electrostatic field configuration. $A$ small test charge is placed at a null point (i.e.,where $E = 0$) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
$(b)$ Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

Consider two points $1$ and $2$ in a region outside a charged sphere. These two points are not very far away from the sphere. If $\overrightarrow{E}$ and $V$ represent the electric field vector and the electric potential respectively,which of the following is not possible?