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 $q V =\frac{1}{2} m v^{2}$
$v =\sqrt{\frac{2 q V}{m}}$
$q v B=q E \Rightarrow B=\frac{E}{V}$
$B =\frac{E}{\sqrt{\frac{2 q V}{m}}}=\frac{E \sqrt{m}}{\sqrt{2 q V}}$
$\frac{B_{2}}{B_{1}}=\frac{E \sqrt{m_{e}}}{\sqrt{2 e V}}$ and $B_{2}=\frac{E \sqrt{m_{\mu}}}{\sqrt{2 e V}}$
$\frac{B_{2}}{B_{1}} =\sqrt{\frac{m_{\mu}}{m_{e}}}$
$B_{1} =\sqrt{208}=14.4$
$B_{2} =14.4 B_{1}$