In the figure shown,the distance from point $A$ to the point where the electric field intensity is zero is .......... $cm$.

$A$ ring of charge with radius $R = 0.5\, m$ having a gap of length $l = 0.02\, m$,carries a total charge of $Q = +1\, C$. The electric field at the centre is

Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown in the figure. Three charges are $+Q$ and three are $-Q$ arranged alternately. The electric field intensity at a point on the line passing through the centre $O$ and perpendicular to the plane of the figure at a large distance $x (x \gg a)$ from $O$ is (Let $\frac{1}{4 \pi \epsilon_0} = k$):

Two large circular discs separated by a distance of $0.01 \ m$ are connected to a battery via a switch as shown in the figure. Charged oil drops of density $900 \ kg \ m^{-3}$ are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity,the switch is closed to apply a voltage of $200 \ V$ across the discs. As a result,an oil drop of radius $8 \times 10^{-7} \ m$ stops moving vertically and floats between the discs. The number of electrons present in this oil drop is (neglect the buoyancy force,take acceleration due to gravity $g = 10 \ m \ s^{-2}$ and charge on an electron $e = 1.6 \times 10^{-19} \ C$):

Two point electric charges $+10^{-8} \text{ C}$ and $-10^{-8} \text{ C}$ are placed $0.1 \text{ m}$ apart. Find the magnitude of the total electric field at the centre of the line joining the two charges.

Two infinitely long parallel wires have linear charge densities $\lambda_1$ and $\lambda_2$ respectively. They are placed at a distance $R$ apart. The force per unit length on the wires will be ......