The maximum value of the electric field on the axis of a charged ring having charge $Q$ and radius $R$ is:

$A$ spherical conductor of radius $2 \text{ cm}$ is uniformly charged with $3 \text{ nC}$. What is the electric field at a distance of $3 \text{ cm}$ from the center of the sphere?

Two point charges $-10 \mu C$ and $+5 \mu C$ are situated on the $X$-axis at $x=0$ and $x=\sqrt{2} \ m$. The point along the $X$-axis where the electric field becomes zero is:

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

$A$ negative charge $-q$ is placed at the midpoint between two fixed equal positive charges $Q$, separated by a distance $2d$. If the negative charge is given a small displacement $x$ $(x \ll d)$ perpendicular to the line joining the positive charges, how will the net force $(F)$ acting on it approximately depend on $x$?

Three charged particles $A, B$ and $C$ with charges $-4q, 2q$ and $-2q$ are present on the circumference of a circle of radius $d$. The charged particles $A, C$ and the centre $O$ of the circle form an equilateral triangle as shown in the figure. The electric field at $O$ along the $x$-direction is