Electrostatics Ques 31
- An electron of mass $m_{e}$, initially at rest, moves through a certain distance in a uniform electric field in time $t_{1}$. A proton of mass $m_{p}$, also, initially at rest, takes time $t_{2}$ to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio $t_{2} / t_{1}$ is nearly equal to
(1997, 1M)
(a) 1
(b) $\left(m_{p} / m_{e}\right)^{1 / 2}$
(c) $\left(m_{e} / m_{p}\right)^{1 / 2}$
(d) 1836
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Answer:
Correct Answer: 31.(b)
Solution:
Formula:
Coulomb Force Between Two Point Charges:
- Electrostatic force, $F_{e}=e E$ (for both the particles)
But acceleration of electron, $a_{e}=F_{e} / m_{e}$ and
acceleration of proton, $a_{p}=F_{e} / m_{p}$
$$ S=\frac{1}{2} a_{e} t_{1}^{2}=\frac{1}{2} a_{p} t_{2}^{2} \Rightarrow \therefore \quad \frac{t_{2}}{t_{1}}=\sqrt{\frac{a_{e}}{a_{p}}}=\sqrt{\frac{m_{p}}{m_{e}}} $$
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