An electron and a proton are moving on straight parallel paths with same velocity. They enter a…

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?
  1. They will never come out of the magnetic field region
  2. They will come out travelling along parallel paths
  3. They will come out at the same time
  4. They will come out at different times

Solution

$\quad r=\frac{m v}{B q}$ or $\quad r \propto m$ $\therefore r_e < r_p$ as $m_e < m_p$ Further, $\quad T=\frac{2 \pi m}{B q}$ or $\quad T \propto m$
$ \begin{aligned} \therefore \quad T_e & < T_p \\ t_e & =\frac{T_e}{2} \end{aligned} $ and or $\quad t_e < t_p$ $\therefore$ Correct options are (b) and (d). Note In JEE 2011, official answer key, correct options were given bc, bd, bcd, here student should realise that both the electron and proton enter the magnetic field at the same time or at different times. Analysis of Question (i) Question is simple. (ii) In the situation given above particle will never complete the circle unless magnetic field is all around

Asked in: JEE Advanced 2011 (Paper 1)

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