Two negative charges of equal magnitude are located in the $xy$-plane as shown in the figure. The direction of the electric field at point $P$ is

$A$ ring of radius $R$ is charged uniformly with a charge $+Q$. The electric field at a point on its axis at a distance $r$ from any point on the ring will be

$A$ charge $10^{-9} \ C$ is located at the origin of a coordinate system and another charge $Q$ at $(2, 0, 0) \ m$. If the $Y$-component of the electric field at $(3, 1, 1) \ m$ is zero,calculate the value of $Q$.

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 $e = 1.6 \times 10^{-19} \ C$):

$A$ wire of length $L$ has a charge $Q$ distributed uniformly along its length. The wire is bent in the shape of a semicircle. The magnitude of the electric field at the centre of curvature of the semicircle is

Two point charges $(+Q)$ and $(-2Q)$ are placed at distances $a$ and $2a$ respectively from the origin on the $X$-axis. At what distance from the origin is the electric field zero?