Electric Charges and Fields - Result Question 15

15. An electron falls from rest through a vertical distance $h$ in a uniform and vertically upward directed electric field $E$. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance $h$. The time of fall of the electron, in comparison to the time of fall of the proton is

[2018]

(a) smaller

(b) 5 times greater

(c) equal

(d) 10 times greater

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Answer:

Correct Answer: 15. (a)

Solution:

  1. (a) As we know, $F=qE=ma$

$\Rightarrow a=\frac{q E}{m}$

$h=\frac{1 q E}{2 m} t^{2}$

$\therefore \quad t=\sqrt{\frac{2 h m}{q E}}$

i.e., time $t \propto \sqrt{m}$ as ’ $q$ ’ is same for electron and proton.

Since, electron has smaller mass so it will take smaller time.