Two positrons $(e^+)$ and two protons $(p)$ are kept on four corners of a square of side $a$ as shown in figure. The mass of proton is much larger than the mass of positron. Let $q$ denotes the charge on the proton as well as the positron then the kinetic energies of one of the positrons and one of the protons respectively after a very long time will be-

Q: Two positrons $(e^+)$ and two protons $(p)$ are kept on four corners of a square of side $a$ as shown in figure. The mass of proton is much larger than the mass of positron. Let $q$ denotes the charge on the proton as well as the positron then the kinetic energies of one of the positrons and one of the protons respectively after a very long time will be-

d As mass of proton $>>>$ mass of positron so initial acceleration of positron is much larger than proton. Therefore position reach far away in very short time as compare to proton. $2 \mathrm{K}_{\mathrm{e}^{+}}=\left(\frac{4 \mathrm{kq}^{2}}{\mathrm{a}}+\frac{2 \mathrm{kq}^{2}}{\mathrm{a} \sqrt{2}}\right)-\frac{\mathrm{kq}^{2}}{\mathrm{a} \sqrt{2}}$ $ \Rightarrow {{\rm{K}}_{{{\rm{e}}^ + }}} = \frac{{{{\rm{q}}^2}}}{{2\pi { \in _0}{\rm{a}}}}\left( {1 + \frac{1}{{4\sqrt 2 }}} \right)$ and $2{{\rm{K}}_{\rm{p}}} = \frac{{{\rm{k}}{{\rm{q}}^2}}}{{{\rm{a}}\sqrt 2 }} - 0 \Rightarrow {{\rm{K}}_{\rm{p}}} = \frac{{{{\rm{q}}^2}}}{{8\sqrt 2 \pi { \in _0}{\rm{a}}}}$

Question

A$\frac{{{q^2}}}{{4\pi { \in _0}a}}\left( {1 + \frac{1}{{2\sqrt 2 }}} \right),\frac{{{q^2}}}{{4\pi { \in _0}a}}\left( {1 + \frac{1}{{2\sqrt 2 }}} \right)$
B$\frac{{{q^2}}}{{2\pi { \in _0}a}},\frac{{{q^2}}}{{4\sqrt 2 \pi { \in _0}a}}$
C$\frac{{{q^2}}}{{4\pi { \in _0}a}},\frac{{{q^2}}}{{4\pi { \in _0}a}}$
D$\frac{{{q^2}}}{{2\pi { \in _0}a}}\left( {1 + \frac{1}{{4\sqrt 2 }}} \right),\frac{{{q^2}}}{{8\sqrt 2 \pi { \in _0}a}}$

Diffcult

Download our app
and get started for free

Similar Questions

Download our appand get started for free

Similar Questions

Download our app
and get started for free