Question

What is the trajectory of the charged particle if the initial velocity of the particle is perpendicular to the direction of the magnetic field?

Answer 1

The force acting on the charged particle placed in a magnetic field is given as

$F=q\left(v\times B\right)$

If the velocity is perpendicular to that of the magnetic field then the force acting on the charged particle is perpendicular to that of velocity and magnetic field. There will not be any components of the force. This is possible only when the trajectory of the field is circular.