Question

The minimum velocity $v_0$, such that an electron projected as shown in the figure passes between the plates without touching them (Take mass of electron as m and charge e. E is electric field between the plates) is

• A. $l\sqrt{\frac{md}{eE}}$
• B. $l\sqrt{\frac{eE}{md}}$
• C. $l\sqrt{\frac{eE}{2md}}$
• D. $\frac {1}{2} \sqrt{\frac{md}{eE}}$

Answer 1

Answer: (B)

$a_{y}=\frac{qE}{m}=\frac{eE}{m}$
$\frac{d}{2} = 0+\frac{1}{2}a_{y}t^{2}$
$t = \sqrt{\frac{d}{a_{y}}}$
So, I = $v_ot$
$v_{o} =\frac{l_{o}}{t}=\frac{l}{\sqrt{\frac{d}{a_{y}}}}=\frac{l\sqrt{a_{y}}}{\sqrt{d}}=l\sqrt{\frac{eE}{md}}$