question_answer

The particle of mass m and charge q will touch the infinitely large plate of uniform charge density \[\sigma \] if its velocity v is more than: \[\{\text{Give}\,\,\text{that }\sigma \,\,q\,\,>0\}\]

A) 0                                 

B) \[\sqrt{\frac{2\,\sigma qd}{m{{\in }_{0}}}}\]

C) \[\sqrt{\frac{\sigma qd}{m{{\in }_{0}}}}\]          

D) none of these

Correct Answer: C

Solution :

\[E=\frac{\sigma }{2{{\varepsilon }_{0}}}\]

\[F=\frac{\sigma q}{2{{\varepsilon }_{0}}}\]

\[a=\frac{\sigma q}{2{{\varepsilon }_{0}}m}\]

\[{{v}_{2}}{{u}^{2}}+2as\]

\[{{0}^{2}}={{v}^{2}}+2\,\,\left( \frac{\sigma q}{2{{\varepsilon }_{0}}m} \right)d\]     \[\Rightarrow \]            \[v=\sqrt{\frac{\sigma qd}{{{\varepsilon }_{0}}m}}\]