Positive and negative point charges of equal magnitude are kept at $\left(0,0, \frac{a}{2}\right)$ and $\left(0,0, \frac{-a}{2}\right)$, respectively. The work done by the electric field when another positive point charge is moved from $(-a, 0,0)$ to $(0, a, 0)$ is

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be.

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

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

An electron (charge = $1.6 \times {10^{ - 19}}$ $coulomb$) is accelerated through a potential of $1,00,000$ $volts$. The energy required by the electron is