Two insulting plates are both uniformly charged in such a way that the potential difference between them is `V_2-V_1=20V`. (i.e., plate 2 is at a higher potential). The plates are separated by `d=0.1m` and can be treated as infinity large. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2? (`e=1.6xx10^-19C`, `m_e=9.11xx10^-31kg`)

Options

A. `7.02 xx10^(12) m//s`
B. `1.87 xx10^(6) m//s`
C. `32 xx10^(-19) m//s`
D. `2.65 xx10^(6) m//s`

Answer

D

Explanation

`E=20/(0.1) = 200 V//m`
`a=(eE)/m,v^2 =u^2+2as impliesv^2 = 2xx(eE)/(m) xx0.1`
`=sqrt((2xx1.6 xx10^(-19)xx200)/(9.11xx10^(-31))xx0.1)=2.65 xx10^6m//s`
Aliter :
`1/2 mv^2 =qV`
`impliesV=sqrt((2xx1.6 xx10^(-19)xx20)/(9.11 xx10^(-31)))=2.65 xx10^6m//s`