Question

A pair of parallel metal plates are kept with a separation '$d$'. One plate is at a potential $+V$ and the other is at ground potential. A narrow beam of electrons enters the space between the plates with a velocity $v_0$ and in a direction parallel to the plates. What will be the angle of the beam with the plates after it travels an axial distance $L$?

• A. ${\tan }^{-1}\left(\frac{eVL}{md{v}_0}\right)$
• B. ${\tan }^{-1}\left(\frac{eVL}{md{v}_0^2}\right)$
• C. ${\sin }^{-1}\left(\frac{eVL}{md{v}_0}\right)$
• D. ${\text{con}}^{-1}\left(\frac{eVL}{md{v}_0^2}\right)$

Answer 1

Answer: (B)

$t=\frac{L}{v_0}$
$v_y=\frac{e}{m}\cdot v\cdot d\times \frac{L}{v_0}=\frac{evL}{md{v}_0}$
$\tan \theta =\frac{v_y}{v_x}=\frac{evL}{md{v}_0\cdot v_0}$
$\Rightarrow \theta ={\tan }^{-1}\left(\frac{evL}{md{v}_0^2}\right)$