-->

Electric Charges And Fields

Question

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

Smaller

5 times greater

Equal

10 times greater

Solution

Smaller

As we know, F = qE = ma
$\Rightarrow a = \frac{q E}{m} h = \frac{I q E}{2 m} t^{2} t = \sqrt{\frac{2 h m}{q E}}$

i.e., time $t \propto \sqrt{m}$ as 'q' is the same for electron and proton. Since the electron has a smaller mass so it will take a smaller time.