Question

In Thomson experiment of finding $\frac{e}{m}$ for electrons, beam of electrons is replaced by that of muons (particle with same charge as of electrons but mass $208$ times that of electrons). No deflection condition in this case satisfied, if

• A. $B$ is increased $208$ times
• B. $E$ is increased $208$ times
• C. $B$ is increased $14.4$ times
• D. None of the above

Answer 1

Answer: (C)

We have $qV=\frac{1}{2}m{v}^2$
$v=\sqrt{\frac{2qV}{m}}$
$qvB=qE\Rightarrow B=\frac{E}{V}$
$B=\frac{E}{\sqrt{\frac{2qV}{m}}}=\frac{E\sqrt{m}}{\sqrt{2qV}}$
$\frac{B_2}{B_1}=\frac{E\sqrt{m_e}}{\sqrt{2eV}}$ and $B_2=\frac{E\sqrt{m_{\mu }}}{\sqrt{2eV}}$
$\frac{B_2}{B_1}=\sqrt{\frac{m_{\mu }}{m_e}}$
$B_1=\sqrt{208}=14.4$
$B_2=14.4B_1$