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. (a)`2.65 xx10^6 ms^(-1)`
B. (b)`7.02 xx10^12 ms^(-1)`
C. (c)`1.87 xx10^6 ms^(-1)`
D. (d)`32 xx10^19 ms^(-1)`

Answer

A

Explanation

Since `V_2 gt V_1`so electric field will point from plate 2 to plate 1.
The electron will experience an electric force, opposite to the direction of electric field and hence move towards the plate 2. Use work-energy theorem to find speed of electron when it strikes the plate 2.
`therefore (mv^2)/2-0=e (V_2-V_1)` where v is the required speed
`implies (9.11 times 10^-31)/2 v^2=1.6 times 10^-19 times 20 or v=sqrt((1.6 times 10^-19 times 40)/(9.11 times 10^-31))=2.65 times 10^6 ms^-1`