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)

in a trajectory represented as $y=a{x}^2$

At the position $X$, we have
Time taken by an electron $t=\frac{x}{v}.....\left(i\right)$
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
$y=a{x}^2\left(Parabola\right)$.