A particle of mass $m$ and charge $q$ is placed at rest in a uniform electric field $E$ and then released. The kinetic energy attained by the particle after moving a distance $y$ is
$qE{y^2}$
$q{E^2}y$
$qEy$
${q^2}Ey$
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 ......... $J$
A positive point charge is released from rest at a distance $r_0$ from a positive line charge with uniform density. The speed $(v)$ of the point charge, as a function of instantaneous distance $r$ from line charge, is proportional to
A particle of mass $m$ having negative charge $q$ move along an ellipse around a fixed positive charge $Q$ so that its maximum and minimum distances from fixed charge are equal to $r_1$ and $r_2$ respectively. The angular momentum $L$ of this particle is
In a hydrogen atom, the electron and proton are bound at a distance of about $0.53\; \mathring A:$
$(a)$ Estimate the potential energy of the system in $eV$, taking the zero of the potential energy at infinite separation of the electron from proton.
$(b)$ What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)?$
$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06\;\mathring A$ separation?
A particle $A$ has charge $+q$ and particle $B$ has charge $+4 q$ with each of them having the same mass $m$. When allowed to fall from rest through the same electric potential difference, the ratio of their speeds $\frac{V_A}{V_B}$ will become