Two identical balls having like charges $Q_1$ and $Q_2$ are placed at a certain distance $r$ apart and repel each other with a force $F_1$. They are brought into contact and then moved apart to a distance equal to half their initial separation $(r/2)$. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is

Two electric charges $+2 \mu C$ and $-4 \mu C$ are separated by a distance $3 \ m$ in air. At a point $P$ located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field at point $P$ (in $NC^{-1}$) is (in $,000$)

$A$ toy car with charge $q$ moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\vec E$. Due to the force $q\vec E$,its velocity increases from $0$ to $6\, m s^{-1}$ in one second. At that instant,the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between $0$ to $3$ seconds are respectively:

The surface of a planet is found to be uniformly charged. When a particle of mass $m$ and no charge is thrown at an angle from the surface of the planet,it has a parabolic trajectory as in projectile motion with horizontal range $L$. $A$ particle of mass $m$ and charge $q$,with the same initial conditions,has a range $L/2$. The range of a particle of mass $m$ and charge $2q$,with the same initial conditions,is:

The electric field $E$ is measured at a point $P(0, 0, d)$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. List-$I$ contains different relations between $E$ and $d$. List-$II$ describes different electric charge distributions,along with their locations. Match the functions in List-$I$ with the related charge distributions in List-$II$.

List-$I$	List-$II$
$P$. $E$ is independent of $d$	$1$. $A$ point charge $Q$ at the origin
$Q$. $E \propto \frac{1}{d}$	$2$. $A$ small dipole with point charges $Q$ at $(0, 0, l)$ and $-Q$ at $(0, 0, -l)$. Take $2l \ll d$.
$R$. $E \propto \frac{1}{d^2}$	$3$. An infinite line charge coincident with the $x$-axis,with uniform linear charge density $\lambda$
$S$. $E \propto \frac{1}{d^3}$	$4$. Two infinite wires carrying uniform linear charge density parallel to the $x$-axis. The one along $(y=0, z=l)$ has a charge density $+\lambda$ and the one along $(y=0, z=-l)$ has a charge density $-\lambda$. Take $2l \ll d$
	$5$. Infinite plane with uniform surface charge density

Four charges $2C, -3C, -4C$ and $5C$ are placed at the corners of a square. Which of the following statements is true for the point of intersection of the diagonals?