If the net electric field at point $\mathrm{P}$ along $\mathrm{Y}$ axis is zero, then the ratio of $\left|\frac{q_2}{q_3}\right|$ is $\frac{8}{5 \sqrt{x}}$, where $\mathrm{x}=$. . . . . .

An infinite number of electric charges each equal to $5\, nC$ (magnitude) are placed along $X$-axis at $x = 1$ $cm$, $x = 2$ $cm$ , $x = 4$ $cm$ $x = 8$ $cm$ ………. and so on. In the setup if the consecutive charges have opposite sign, then the electric field in Newton/Coulomb at $x = 0$ is $\left( {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\,N - {m^2}/{c^2}} \right)$

The three charges $q / 2, q$ and $q / 2$ are placed at the corners $A , B$ and $C$ of a square of side ' $a$ ' as shown in figure. The magnitude of electric field $(E)$ at the comer $D$ of the square, is

A charged oil drop is suspended in a uniform field of $3 \times$ $10^{4} V / m$ so that it neither falls nor rises. The charge on the drop will be $.....\times 10^{-18}\; C$

(take the mass of the charge $=9.9 \times 10^{-15} kg$ and $g=10 m / s ^{2}$ )

As shown in the figure, a particle A of mass $2\,m$ and carrying charge $q$ is connected by a light rigid rod of length $L$ to another particle $B$ of mass $m$ and carrying charge $-q.$ The system is placed in an electric field $\vec E$ . The electric force on a charge $q$ in an electric field $\vec E$ is $\vec F = q \vec E $ . After the system settles into equilibrium, one particle is given a small push in the transverse direction so that the rod makes a small angle $\theta_0$ with the electric field. Find maximum tension in the rod.

Figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero