Question 5: What will be the path of a charged particle moving in a uniform magnetic field at any arbitrary angle with the field?
Let the charged particle enters the magnetic field so that the angle between v and B is θ. The velocity of the particle can be resolved into its rectangular components such that
vx = vcosθ
This component of the velocity is along the magnetic field B and keeps the particle move in the direction of B.
vy = vsinθ
This component of the velocity is perpendicular to the magnetic field and causes the particle move in the direction perpendicular to B.
The combined effect of the two component velocities is that the particle moves in a helical path.