question_answer

A charged particle enters in a magnetic field H with its initial velocity making an angle of \[{{45}^{o}}\] with H. The path of the particle will be

A) an ellipse    

B)        a straight line

C) a circle           

D)        a helical.

Correct Answer: D

Solution :

                When a charged particle enters a magnetic field, the particle experiences a Lorentz force given by \[\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B}),\]which act in a direction perpendicular to    both \[\overrightarrow{v}\]and \[\overrightarrow{B}\]. Now since the initial velocity of the particle makes an angle \[{{45}^{o}}\] with the magnetic field, it will be having a velocity component parallel to \[\overrightarrow{B}\] and another component perpendicular to \[\overrightarrow{B}\]. The parallel component of velocity is going to experience no force, So it will remain the same but as the perpendicular component will experience a constant force in the normal plane, hence the particle will finally move in a helical path.