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
A$\frac{{Z{e^2}}}{{2\pi {\varepsilon _0}m{v^2}}}$
B$\frac{{Ze}}{{4\pi {\varepsilon _0}m{v^2}}}$
C$\frac{{Z{e^2}}}{{8\pi {\varepsilon _0}m{v^2}}}$
D$\frac{{Ze}}{{8\pi {\varepsilon _0}m{v^2}}}$
Medium
Download our app for free and get started
A$\frac{{Z{e^2}}}{{2\pi {\varepsilon _0}m{v^2}}}$
a (a) Suppose distance of closest approach is $r$, and according to energy conservation applied for elementary charge.
Energy at the time of projection $=$ Energy at the distance of closest approach
$==>$ $\frac{1}{2}m{v^2} = \frac{1}{{4\pi {\varepsilon _0}}}.\frac{{(Ze).e}}{r} \Rightarrow r = \frac{{Z{e^2}}}{{2\pi {\varepsilon _0}m{v^2}}}$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
The capacity of a condenser in which a dielectric of dielectric constant $5$ has been used, is $C$. If the dielectric is replaced by another with dielectric constant $20$, the capacity will become
A parallel plate capacitor of plate area $A$ and plate seperation $d$ is charged to potential difference $V$ and then the battery is disconnected. Aslab of dielectric constant $K$ is then inserted between the plates of the capacitor so as to fill the space between the plates. If $Q, E$ and $W$ denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted) and the work done on the system, in question, in the process of inserting the slab, then
The two metallic plates of radius $r$ are placed at a distance $d$ apart and its capacity is $C$. If a plate of radius $r/2$ and thickness $d$ of dielectric constant $6$ is placed between the plates of the condenser, then its capacity will be
A circuit has a section $AB$ as shown in the figure. If the potential difference between points $A$ and $B$ is $V\, volt$, then potential difference across $C_1$ is
Separation between the plates of a parallel plate capacitor is $d$ and the area of each plate is $A$. When a slab of material of dielectric constant $k$ and thickness $t(t < d)$ is introduced between the plates, its capacitance becomes