A small sphere of mass $m =\ 0.5\, kg$ carrying a positive charge $q = 110\  \mu C$ is connected with a light, flexible and inextensible string of length $r = 60 \ cm$ and whirled in a vertical circle. If a vertically upwards electric field of strength $E = 10^5 NC^{-1}$ exists in the space, The minimum velocity of  sphere required at highest point so that it may just complete the circle........$m/s$  $(g = 10\, ms^{-2})$

In Millikan's experiment, an oil drop having charge $q$ gets stationary on applying a potential difference $V$ in between two plates separated by a distance $d$. The weight of the drop is

Two equal charges $q$ are placed at a distance of $2a$ and a third charge $ - 2q$ is placed at the midpoint. The potential energy of the system is

There is a uniform spherically symmetric surface charge density at a distance $R_0$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed $V(R(t))$ of the distribution as a function of its instantaneous radius $R(t)$ is

In free space, a particle $A$ of charge $1\,\mu C$ is held fixed at a point $P.$ Another particle $B$ of the same charge and mass $4\,\mu g$ is kept at a distance of $1\,mm$ from $P$. If $B$ is released, then its velocity at a distance of $9\,mm$ from $P$ is [ Take $\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N{m^2}{C^{ - 2}}$ ]

A bullet of mass $2\, gm$ is having a charge of $2\,\mu C$. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of $10\,m/s$