Two identical charged particles,each having a mass $10 \, g$ and charge $2.0 \times 10^{-7} \, C$,are placed on a horizontal table with a separation of $L$ between them such that they stay in limiting equilibrium. If the coefficient of friction between each particle and the table is $0.25$,find the value of $L$ in $cm$. [Use $g = 10 \, m/s^2$]

Two particles $X$ and $Y$, of equal mass and with unequal positive charges, are free to move and are initially far away from each other. With $Y$ at rest, $X$ begins to move towards it with initial velocity $u$. After a long time, finally

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?

Two charges,each equal to $q$,are kept at $x = -a$ and $x = a$ on the $x$-axis. $A$ particle of mass $m$ and charge $q_0 = \frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y << a)$ along the $y$-axis,the net force acting on the particle is proportional to

An infinitely long thin wire,having a uniform charge density per unit length of $5 \text{ nC/m}$,is passing through a spherical shell of radius $1 \text{ m}$,as shown in the figure. $A$ $10 \text{ nC}$ charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static,the magnitude of the potential difference between points $P$ and $R$,in Volt,is. . . .
[Given: In $SI$ units $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9, \ln 2=0.7$. Ignore the area pierced by the wire.]

An oil drop carries six electronic charges,has a mass of $1.6 \times 10^{-12} \text{ g}$ and falls with a terminal velocity in air. The magnitude of the vertical electric field required to make the drop move upward with the same speed as it was formerly moving is ........$kN/C$.