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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?
Options:
Solution:
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Verified Answer
The correct answers are:
They will come out travelling along parallel paths
,
They will come out at different times
They will come out travelling along parallel paths
,
They will come out at different times
$\quad r=\frac{m v}{B q}$
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.
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.
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