Question

An electron is projected as shown in the figure, with kinetic energy K, at an angle $\theta ={45}^{\circ }$
between two charged plates. Ignore the gravity.
The magnitude of the electric field so that the electron just fails to strike the upper plate is

• A. $\frac{K}{qd}$
• B. $\frac{2K}{qd}$
• C. $\frac{K}{2qd}$
• D. Infinite

Answer 1

The correct option is C $\frac{K}{2qd}$


$H_{max}\le d$, where $H_{max}=$ maximum height electron can travel

$\frac{u^2{\sin }^2\theta }{2a}=d$

$\because \theta ={45}^{\circ }\text{and}a=\frac{eE}{m}$

$u^2\times \frac{1}{2}\frac{m}{2\times eE}=d$

$\frac{1}{2}m\frac{u^2}{2Ee}=d$

$\because \frac{1}{2}m{u}^2=k$

($\frac{k}{2Ee}=d$)

$E=\frac{k}{2ed}$