An electromagnetic wave travels in free space along the x-direction. At a particular point in space and time, $\vec{B} = 2 \times 10^{-7} \hat{j}$ T is associated with this wave. The value of corresponding electric field $\vec{E}$ at this point is _______ V/m.

Two resistors of 200 $\Omega$ and 400 $\Omega$ are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the 400 $\Omega$ resistance. The potential drop across the bulb is ________ V.

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 ________.