Two metal plates (A, B) are kept horizontally with separation of $ \left( \frac{12}{\pi} \right) $ cm, with plate A on the top.

An atomizer jet sprays oil (density 1.5 g/cm³) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials V_A and V_B are required on plates A and B respectively in order to ensure the droplets do not descend. The values of V_A and V_B are ______.

(Neglect the air resistance to the droplets and take g = 10 m/s²)

Two point charges $8\ \mu C$ and $-2\ \mu C$ are located at $x = 2$ cm and $x = 4$ cm, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is ________.

Two charged conducting spheres $S_1$ and $S_2$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S1}$ and $E_{S2}$ respectively. The value of $\dfrac{E_{S1}}{E_{S2}}$ is ________.

Two short electric dipoles A and B having dipole moment $p_1$ and $p_2$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point $x$ is making an angle of $60^{\circ}$ with the line joining points $O$ and $x$. The ratio of the dipole moments $p_2/p_1$ is _________.