question_answer

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

Correct Answer: D

Solution :

 Consider a particle of charge q and mass 222 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         \[y=ut\]                                   ...(ii) 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.