An $\alpha $-particle is accelerated through a potential difference of $200\,V$. The increase in its kinetic energy is…….$eV$

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

$(a)$ In a quark model of elementary particles, a neutron is made of one up quarks [ charge $\frac{2}{3}e$ ] and two down quarks [ charges $ – \frac{1}{3}e$ ]. Assume that they have a triangle configuration with side length of the order of ${10^{ – 15}}$ $m$. Calculate electrostatic potential energy of neutron and compare it with its mass $939$ $Me\,V$. $(b)$ Repeat above exercise for a proton which is made of two up and one down quark.

In the following diagram the work done in moving a point charge from point $P$ to point $A, B$ and $C$ is respectively as $W_A,\, W_B$ and $W_C$, then (there is no charge nearby)

Six charges $+ q ,- q ,+ q ,- q ,+ q$ and $- q$ are fixed at the corners of a hexagon of side $d$ as shown in the figure. The work done in bringing a charge $q _0$ to the centre of the hexagon from infinity is :$\left(\varepsilon_0-\right.$ permittivity of free space)