Two point positive charges are placed at a distance $d$ apart. $A$ third positive charge is placed at a distance $x$ on the perpendicular bisector. For what value of $x$ is the force on the third charge maximum?

$A$ charge $Q$ of mass $m$ revolves around a charge $q$ due to the electrostatic attraction between them. The time period of its motion can be given by the formula:

Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges. Alternate charges $1, 3, 5, 7, 9$ have charge $(+q)$ each, while $2, 4, 6, 8, 10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at the centre of the circle are respectively (Take $V = 0$ at infinity).

The earth's surface has a negative surface charge density of $10^{-9} \; C\;m^{-2}$. The potential difference of $400 \; kV$ between the top of the atmosphere and the surface results (due to the low conductivity of the lower atmosphere) in a current of only $1800 \; A$ over the entire globe. If there were no mechanism of sustaining the atmospheric electric field,how much time (roughly) would be required to neutralize the earth's surface (in $; s$)? (This never happens in practice because there is a mechanism to replenish electric charges,namely the continual thunderstorms and lightning in different parts of the globe). (Radius of earth $= 6.37 \times 10^{6} \; m$.)

$A$ glass rod rubbed with silk is used to charge a gold leaf electroscope and the leaves are observed to diverge. The electroscope thus charged is exposed to $X$-rays for a short period. Then

For the given figure,the direction of the electric field at point $A$ will be .........