Three charges $Q, +q$ and $+q$ are placed at the vertices of a right -angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of $Q$ is
$+q$
$\frac{{ - \sqrt 2 q}}{{\sqrt 2 + 1}}$
$\frac{{ - q}}{{1 + \sqrt 2 }}$
$-2q$
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........$m/s$ $(g = 10\, ms^{-2})$
For equal point charges $Q$ each are placed in the $xy$ plane at $(0, 2), (4, 2), (4, -2)$ and $(0, -2)$. The work required to put a fifth change $Q$ at the origin of the coordinate system will be
In the figure the charge $Q$ is at the centre of the circle. Work done is maximum when another charge is taken from point $P$ to
An electron of mass $m$ and charge $e$ is accelerated from rest through a potential difference $V$ in vacuum. Its final velocity will be