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 $y = ax^2$
• 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, $a=\frac{E_{e}}{2 m v^{2}}$]
So, the trajectory represented as
$y=a x^{2}$ (Parabola)