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 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.