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.
At what distance from the starting point will the electron strike the lower plate?

• A. $d$
• B. $2d$
• C. $3d$
• D. $4d$

Answer 1

The correct option is D $4d$

Let R be the range of the projectile.
$H_{max}\le d$, where $H_{max}=$ maximum height electron can travel

$⟹\frac{u^2{\sin }^2\theta }{2a}=d$

As $\theta ={45}^{\circ }$
$⟹d=\frac{u^2}{4a}$......(i)
We know that range R is given by
$R=\frac{u^{2}sin2\theta }{a}$
$⟹R=\frac{u^2}{a}$.......................(ii)
$\therefore$ From (i) and (ii) we can say
$R=4d$