The minimum velocity v0, 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

Question

The minimum velocity v0, 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√(md/eE) (B) l√(eE/md) (C) l√(eE/2md) (D)  (1/2) √(md/eE)

Tardigrade Admin · Accepted Answer

ay=(qE/m)=(eE/m) (d/2) = 0+(1/2)ayt2 t = √(d/ay) So, I = vot vo =(lo/t)=(l/√(d)ay)=(l√ay/√d)=l√(eE/md)

Q. 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

$l \frac{m d}{e E}$

$l \frac{e E}{m d}$

$l \frac{e E}{2 m d}$

$\frac{1}{2} \frac{m d}{e E}$

$a_{y} = \frac{qE}{m} = \frac{e E}{m}$
$\frac{d}{2} = 0 + \frac{1}{2} a_{y} t^{2}$
$t = \frac{d}{a _{y}}$
So, I = $v_{o} t$
$v_{o} = \frac{l _{o}}{t} = \frac{l}{\frac{d}{a _{y}}} = \frac{l a _{y}}{d} = l \frac{e E}{m d}$

Q. The minimum velocity v0​, 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

leEmd​​

lmdeE​​

l2mdeE​​

21​eEmd​​