Electrostatics Question 386
Question: An electron of mass $ m _{e} $ initially at rest moves through a certain distance in a uniform electric field in time $ t _{1} $ . A proton of mass $ m _{p} $ also initially at rest takes time $ t _{2} $ to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of $ t _{2}/t _{1} $ is nearly equal to [IIT 1997 Cancelled]
Options:
A) 1
B) $ {{(m _{p}/m _{e})}^{1/2}} $
C) $ {{(m _{e}/m _{p})}^{1/2}} $
D) 1836
Show Answer
Answer:
Correct Answer: B
Solution:
For electron $ s=\frac{eE}{m _{e}}\times t _{1}^{2} $ , For proton $ s=\frac{eE}{m _{p}}\times t _{2}^{2} $
$ \frac{t _{2}^{2}}{t _{1}^{2}}=\frac{m _{p}}{m _{e}}\Rightarrow \frac{t _{2}}{t _{1}}=\sqrt{\frac{m _{p}}{m _{e}}}={{( \frac{m _{p}}{m _{e}} )}^{1/2}} $
