Question

A particle of charge q is moving with velocity v in the presence of crossed electric field E and magnetic field B as shown. Write the condition under which the particle will continue moving along x-axis. How would the trajectory of the particle be affected if the electric field is suddenly switched off?

Answer 1

A charged particle continue to moving along x-axis the net force exerted by electric field and magnetic field should be in opposite direction and canceled out so velocity is determined by

$qE=qvB$

$v=\frac{E}{B}$

In the absence of electric field the tarjectory of the charged particle in the presence of magnetic field is in the circular path because the force is always acting at the center of the circular path of the charged particle.