Question

An electron moving with a constant velocity $v$ along $X-$axis enters a uniform electric field applied along $Y-$axis. Then the electron moves

• A. with uniform acceleration along Y-axis
• B. without any acceleration along Y-axis
• C. in a trajectory represented as $y=a{x}^2$
• D. in a trajectory represented as y -ax
• E. with uniform deceleration along X-axis

Answer 1

Answer: (C)

At the position $X$, we have

Time taken by an electron $t=\frac{X}{V}$ ...(i)
and displacement of an electron
$y=\frac{1}{2}a{t}^2=\frac{1}{2}\frac{E_e}{m}{t}^2$
From Eq. (i), $y=\frac{1}{2}\frac{E_e}{m}\frac{x^2}{v^2}$
$\Rightarrow y=a{x}^2$
[$\therefore$ acceleration, $a=\frac{E_e}{2m{v}^2}$]
So, the trajectory represented as
$y=a{x}^2$ (Parabola)