Electrostatic potential energy of given system will be

A particle of charge $q$ and mass $m$ is subjected to an electric field $E = E _{0}\left(1- ax ^{2}\right)$ in the $x-$direction, where $a$ and $E _{0}$ are constants. Initially the particle was at rest at $x=0 .$ Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is

A proton has a mass $1.67 \times 10^{-27} \,kg$ and charge $+1.6 \times 10^{-19} \,C$. If the proton is accelerated through a potential difference of million volts, then the kinetic energy is ......... $J$

An electron enters in high potential region ${V_2}$ from lower potential region ${V_1}$ then its velocity

A uniformly charged thin spherical shell of radius $\mathrm{R}$ carries uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $\mathrm{F}$ (see figure). $\mathrm{F}$ is proportional to

In the electric field of a point charge $q$, a certain charge is carried from point $A$ to $B, C, D$ and $E$. Then the work done