An infinite number of charges,each equal to $0.2\,\mu C$,are arranged in a line at distances $1\,m, 2\,m, 4\,m, 8\,m, \dots$ from a fixed point. The potential at the fixed point is $......\,kV$.

$A$ sphere with charge $Q$ is placed concentrically inside an uncharged spherical shell. The potential difference between them is $V$. Now,if a charge of $-3Q$ is given to the spherical shell,what will be the potential difference between them?

Two metal spheres of radii $R_1$ and $R_2$ are charged to the same potential. The ratio of charges on the spheres is

Two point charges are located on the $x$-axis. $q_1 = -1 \ \mu C$ at $x = 0$ and $q_2 = +1 \ \mu C$ at $x = 1 \ m$. Find the work done in bringing a third charge $q_3 = +1 \ \mu C$ from infinity to $x = 2 \ m$.

Two positive charges $Q$ and $4Q$ are placed at points $A$ and $B$ respectively, where $B$ is at a distance $d$ units to the right of $A$. The total electric potential due to these charges is minimum at point $P$ on the line segment joining $A$ and $B$. What is the distance of $P$ from $A$?

$A$ ball of mass $1\, g$ and charge $10^{-8}\, C$ moves from a point $A$,where the potential is $600\, V$,to a point $B$,where the potential is $0\, V$. The velocity of the ball at point $B$ is $20\, cm/s$. The velocity of the ball at point $A$ will be: