Two charged particles P and Q, having the same charge but different...

Question

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 times $t_P$ and $t_Q$ respectively. Neglecting gravity, find the ratio $t_P/t_Q$.

Accepted Answer

Step 1: Acceleration $a = qE/m$ (same $q$, $E$ for both).

Step 2: From rest, $s = \frac{1}{2}at^2 \Rightarrow t = \sqrt{2s/a} = \sqrt{2sm/(qE)}$, so $t\propto\sqrt m$.

Step 3: $\dfrac{t_P}{t_Q} = \sqrt{\dfrac{m_P}{m_Q}}$.

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