If an $\alpha$-particle and a proton are accelerated from rest by a potential difference of 1 megavolt then the ratio of their kinetic energy will be

A proton is about $1840$ times heavier than an electron. When it is accelerated by a potential difference of $1\, kV$, its kinetic energy will be......$keV$

There exists an electric field of magnitude $E$ in $x$-direction. If the work done in moving a charge of $0.2 \,C$ through a distance of $2 \,m$ along a line making an angle $60^{\circ}$ with $x$-axis is $4 \,J$, then the value of $E$ is ........ $N / C$

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

This questions has statement$-1$ and statement$-2$. Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $R$ has a uniformly
positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.

Statement$ -1$ : When a charge $q$ is take from the centre of the surface of the sphere its potential energy changes by  $\frac{{q\rho }}{{3{\varepsilon _0}}}$

Statement$ -2$ : The electric field at a distance $r(r < R)$  from centre of the sphere is $\frac{{\rho r}}{{3{\varepsilon _0}}}$

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