An electron of mass $m$ and charge $e$ is accelerated from rest through a potential difference $V$ in vacuum. The final speed of the electron will be

A conducting sphere of radius a has charge $Q$ on it. It is enclosed by a neutral conducting concentric spherical shell having inner radius $2a$ and outer radius $3a.$ Find electrostatic energy of system.

A point chargr $Q$ is fixed A small charge $q$ and mass $m$ is given a velocity $v_0$ from infinity & perpendicular distance $r_0$ as shown. If distance of closest approach is $r_0/2$. The value of $q$ is [Given $mv_0^2 = \frac{{{Q^2}}}{{4\pi { \in _0}\,{r_0}}}$]

Three point charges $Q, 4Q $ and $16Q $ are placed on a straight line $9$ $cm$ long. Charges are placed in such a way that the system has minimum potential energy. Then

Three point charges $q, q$ and $-2 q$ are placed at the corners of an equilateral triangle of side '$L$'. Calculate work done by extemal force in moving all the charges far apart without acceleration

The diagram shows a small bead of mass $m$ carrying charge $q$. The bead can freely move on the smooth fixed ring placed on a smooth horizontal plane. In the same plane a charge $+Q$ has also been fixed as shown. The potential atthe point $P$ due to $+Q$ is $V$. The velocity with which the bead should projected from the point $P$ so that it can complete a circle should be greater than