Electric field

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Question

A proton and an $α -$ particle start from rest in a uniform electric field, then the ratio of times of flight to travel same distance in the field is

Solution

$F = m a \Rightarrow q E = m a \Rightarrow a = \frac{q E}{m} N o w, y = \frac{1}{2} a t^{2} \Rightarrow y = \frac{E q t^{2}}{2 m} \Rightarrow t^{2} \propto \frac{m}{q} {(\frac{t_{p}}{t_{α}})}^{2} = \frac{m_{p}}{m_{α}} \times \frac{q_{α}}{q_{p}} = \frac{t_{p}}{t_{α}} = \sqrt{\frac{1}{4} \times \frac{2}{1}} = \sqrt{\frac{1}{2}} t_{p} : t_{α} = 1 : \sqrt{2}$

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Electric field

Remember concepts with our Masterclasses.

A proton and an α-particle start from rest in a uniform electric field, then the ratio of times of flight to travel same distance in the field is

F= ma ⇒qE=ma ⇒a=qEm Now, y = 12at2 ⇒y=Eqt22m ⇒t2 ∝mq tptα2=mpmα×qαqp =tptα=14×21=12 tp:tα=1:2

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A proton and an $α -$ particle start from rest in a uniform electric field, then the ratio of times of flight to travel same distance in the field is