Two charged particles P and Q , having the same charge but different masses \({m}_{P}\) and \({m}_{Q}\), start from rest…
Two charged particles P and Q , having the same charge but different masses \({m}_{P}\) and \({m}_{Q}\), start from rest and travel equal distances in a uniform electric field \(\vec{E}\) in time \({t}_{P}\) and \({t}_{Q}\) respectively. Neglecting the effect of gravity, the ratio \(\left(\frac{{t}_{P}}{{t}_{Q}}\right)\) is :
\(\sqrt{\frac{{\mathrm{m}}_{\mathrm{P}}}{{\mathrm{m}}_{\mathrm{Q}}}}\)
The acceleration a of each particle is given by Newton’s second law:F=ma and F=qE ⇒a=qE/m.
Thus, the time taken for each particle to travel the same distance is given by the kinematic equation:
d=\(\frac{1}{2}a{t}^{2}\)
⇒t=\(\sqrt{\frac{2d}{a}}\)=\(\sqrt{\frac{2d}{\frac{qE}{m}}}\)
The ratio of times tp and tq for particles P and Q is:\(\sqrt{\frac{{m}_{P}}{{m}_{Q}}}\)
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