Question

An electron moves with a velocity $\overrightarrow{v}$ in an electric field $\overrightarrow{E}$. If the angle between $\overrightarrow{v}$ and $\overrightarrow{E}$ is neither 0 nor $\pi$, then the path followed by the electron is a(an):

• A. straight line
• B. circle
• C. ellipse
• D. parabola

Answer 1

The correct option is D parabola

The perpendicular component of velocity is given by:
$v_y=v\sin \theta$
Now in the X direction, the electron experiences a force of $E(-e)$
So, $F=-eE$
or, $a=\frac{-Ee}{m}$

$\therefore$ velocity in X direction:

$v_x=u+at$ $=vcos\theta -\frac{Ee}{m}\times t$

We know, $y=\int v_{y}dt$ and $x=\int \left(v_x\right)dt$

$\Rightarrow$ $y=v\sin \theta \cdot t,x=vcos\theta \cdot t-\frac{Ee}{m}\frac{t^2}{2}$

Substituting $t=\frac{y}{vsin\theta }$, we get $x=v\cos \theta \frac{y}{vsin\theta }-\frac{Ee}{m_2}\cdot \frac{y^2}{v^{2}si{n}^2\theta }$

$\Rightarrow$ $x=y\cot \theta -\frac{Ee}{2m{v}^{2}si{n}^2\theta }{y}^2$, where $\theta$ is the initial angle of $v$ with $E$.

$\therefore$ path followed is a parabola