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1. Electric Charges and Fields
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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 of ${t_2}/{t_1}$ is nearly equal to
A
$1$
B
${({m_p}/{m_e})^{1/2}}$
C
${({m_e}/{m_p})^{1/2}}$
D
$1836$
(IIT-1997) (AIIMS-2015)
Solution
(b) For electron $s = \frac{{eE}}{{{m_e}}} \times t_1^2$, For proton $s = \frac{{eE}}{{{m_p}}} \times t_2^2$
$\frac{{t_2^2}}{{t_1^2}} = \frac{{{m_p}}}{{{m_e}}}\, \Rightarrow \frac{{{t_2}}}{{{t_1}}} = \sqrt {\frac{{{m_p}}}{{{m_e}}}} = {\left( {\frac{{{m_p}}}{{{m_e}}}} \right)^{1/2}}$
Standard 12
Physics
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