Question

The path of a charge particle after it enters a region of a uniform electrostatic field with velocity perpendicular to the field will be

• A. Straight line
• B. Circular
• C. Helical
• D. Parabolic

Answer 1

Answer: (D)

Consider a particle of charge $q$ and mass $m$ enters a region of uniform electric field $E$.
At any instant $t$, coordinates are
$x=\frac{1}{2}\times \frac{qE}{m}{t}^2$ ...(i)
and $y=ut$
From Eqs. (i)and(ii), we get
$x=\frac{1}{2}\times \frac{qE}{m}\times \frac{Y^2}{u^2}$
$\Rightarrow y^2=\left(\frac{2m{u}^2}{qE}\right)x$
or $y^2=kx$
where, $k=$ constant This is an equation of a parabola.
So, the path of charge particle will be parabola.