Question

A proton and an alpha particle start from rest in a uniform electric field then the ratio of time of flight to travel same distance in the field is?

Answer 1

this may help u..........

Answer 2

Answer:The ratio of time of flight to travel same distance in the field is 1:4.

Explanation:

Mass of the proton = m

Charge of the proton = q

Force of the proton = q E

$qE= ma$......(I)

Where, a is the acceleration of the proton

Mass of the alpha particle = 4 m

Charge of the alpha particle = 2q

Force of the alpha particle = 2qE

$2qE= 4mb$.....(II)

Where, b is the acceleration of alpha particle

Divided equation (I) by equation (II)

$\dfrac{qE}{2qE}=\dfrac{ma}{4mb}$

$\dfrac{a}{b}=\dfrac{2}{1}$

Both particles travel same distance in the field, E

Using equation of motion

$s = ut +\dfrac{1}{2}at^2$

Now, for both particles

$\dfrac{1}{2}a^2t_{a}= \dfrac{1}{2}b^2t_{b}$

$\dfrac{a^2}{b^2}=\dfrac{t_{b}}{t_{a}}$

$\dfrac{t_{b}}{t_{a}}= \dfrac{4}{1}$

$\dfrac{t_{a}}{t_{b}}= \dfrac{1}{4}$

Hence, The ratio of time of flight to travel same distance in the field is 1:4.