| 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: (Given that \[\sigma \,q>0\]) |
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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 :
| \[E=\frac{\sigma }{2{{\varepsilon }_{0}}}:\,\,\,\,F=\frac{\sigma q}{2{{\varepsilon }_{0}}}\] |
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| \[a=\frac{\sigma }{2{{\varepsilon }_{0}}m}\] \[{{v}^{2}}={{u}^{2}}+2as\] |
| \[{{0}^{2}}={{v}^{2}}+2\left( \frac{\sigma q}{2{{\varepsilon }_{0}}m} \right)d\] \[\Rightarrow \,\,\,v=\sqrt{\frac{\sigma qd}{{{\varepsilon }_{0}}m}}\] |
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