Question

An electron enters the region between the plates of a parallel plate capacitor at an angle $\theta$ to the plates. The plate width is I. The plate separation is d. The electron follows the path shown, just missing the upper plate. Neglect gravity. d
Then

• A. $tan\theta =2d/l$
• B. $tan\theta =4d/l$
• C. $tan\theta =8d/l$
• D. the data given is insufficient to find a relation between d, l and $\theta$

Answer 1

The correct option is B $tan\theta =4d/l$

Here, the horizontal range , $R=\frac{2u_x{u}_y}{g}=l...\left(1\right)$ and
maximum height, $H=\frac{u_y^2}{2g}=d....\left(2\right)$
$\left(2\right)/\left(1\right)\Rightarrow \frac{u_y}{4u_x}=\frac{d}{l}$
or $\frac{u_y}{u_x}=\frac{4d}{l}$
or $\frac{\sin \theta }{\cos \theta }=\frac{4d}{l}$
or $\tan \theta =\frac{4d}{l}$