An elementary particle of mass $m$ and charge $ + e$ is projected with velocity $v$ at a much more massive particle of charge $Ze,$ where $Z > 0.$What is the closest possible approach of the incident particle
$\frac{{Z{e^2}}}{{2\pi {\varepsilon _0}m{v^2}}}$
$\frac{{Ze}}{{4\pi {\varepsilon _0}m{v^2}}}$
$\frac{{Z{e^2}}}{{8\pi {\varepsilon _0}m{v^2}}}$
$\frac{{Ze}}{{8\pi {\varepsilon _0}m{v^2}}}$
Four identical charges $ + \,50\,\mu C$ each are placed, one at each corner of a square of side $2\,m$. How much external energy is required to bring another charge of $ + \,50\,\mu C$ from infinity to the centre of the square......$J$ $\left( {{\rm{Given}}\frac{{\rm{1}}}{{{\rm{4}}\pi {\varepsilon _{\rm{0}}}}} = 9 \times {{10}^9}\,\frac{{N{m^2}}}{{{C^2}}}} \right)$
A charged particle $q$ is shot towards another charged particle $Q$ which is fixed, with a speed $v$. It approaches $Q$ upto a closest distance $r$ and then returns. If $q$ were given a speed $2v$, the closest distances of approach would be
Consider the configuration of a system of four charges each of value $+q$ . The work done by external agent in changing the configuration of the system from figure $(1)$ to figure $(2)$ is
A problem of practical interest is to make a beam of electrons turn at $90^o$ corner. This can be done with the electric field present between the parallel plates as shown in the figure. An electron with kinetic energy $8.0 × 10^{-17}\ J$ enters through a small hole in the bottom plate. The strength of electric field that is needed if the electron is to emerge from an exit hole $1.0\ cm$ away from the entrance hole, traveling at right angles to its original direction is $y × 10^5\ N/C$ . The value of $y$ is
Figures $(a)$ and $(b)$ show the field lines of a positive and negative point charge respectively
$(a)$ Give the signs of the potential difference $V_{ P }-V_{ Q } ; V_{ B }-V_{ A }$
$(b)$ Give the sign of the potential energy difference of a small negative charge between the points $Q$ and $P ; A$ and $B$.
$(c)$ Give the sign of the work done by the field in moving a small positive charge from $Q$ to $P$.
$(d)$ Give the sign of the work done by the external agency in moving a small negative charge from $B$ to $A$.
$(e)$ Does the kinetic energy of a small negative charge increase or decrease in going from $B$ to $A?$