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. $\tan ^{-1}\left(\frac{e V L}{m d v_{0}}\right)$
• B. $\tan ^{-1}\left(\frac{e V L}{m d v_{0}^{2}}\right)$
• C. $\sin ^{-1}\left(\frac{e V L}{m d v_{0}}\right)$
• D. $\text{con}^{-1}\left(\frac{e V L}{m d v_{0}^{2}}\right)$

Answer 1

Answer: (B)

$t=\frac{L}{v_{0}}$
$v_{y}=\frac{e}{m} \cdot v \cdot d \times \frac{L}{v_{0}}=\frac{e v L}{m d v_{0}}$
$\tan \theta=\frac{v_{y}}{v_{x}}=\frac{e v L}{m d v_{0} \cdot v_{0}}$
$\Rightarrow \theta=\tan ^{-1}\left(\frac{e v L}{m d v_{0}^{2}}\right)$