An infinite number of charges, each of charge $1 \,\mu C$ are placed on the $x$-axis with co-ordinates $x = 1, 2,4, 8, ....\infty$. If a charge of $1\, C$ is kept at the origin, then what is the net force acting on $1\, C$ charge....$N$

Three charges $+Q, q, +Q$ are placed respectively, at distance, $0, \frac d2$ and $d$ from the origin, on the $x-$ axis. If the net force experienced by $+Q$, placed at $x = 0$, is zero, then value of $q$ is

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

Two free positive charges $4q$ and $q$ are a distance $l$ apart. What charge $Q$ is needed to achieve equilibrium for the entire system and where should it be placed form charge $q$ ?

Two small conducting spheres of equal radius have charges $ + 10\,\mu C$ and $ - 20\,\mu C$ respectively and placed at a distance $R$ from each other experience force ${F_1}$. If they are brought in contact and separated to the same distance, they experience force ${F_2}$. The ratio of ${F_1}$ to ${F_2}$ is

Two identical charged spheres suspended from a common point by two massless strings of lengths $l,$ are initially at a distance $d\;(d < < l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $v.$ Then $v$ varies as a function of the distance $x$ between the spheres, as