Question

Write the expression for the force `vecF` acting on a particle of mass m and charge q moving with velocity `vecV` in a magnetic field `vecB` , Under what conditions will it move in (i) a circular path and (ii) a helical path?

Answer 1

When a charged particle having charge q moves inside a magnetic field `vecB` with velocity `vecV`, it experiences a force
`vecF =q(vecV ×vecB )`
When `vecV` is perpendicular to `vecB` 
The force `vecF` on the charged particle acts as the centripetal force and makes it move along a circular path.
The point charge travels in the plane perpendicular to both `vecV` and `vecB`.

When the component of velocity of the charge particle is parallel to the direction of the force of the electric field, then the force experienced due to that component will be zero, because
F=qvBsin0°=0, and particle will move in a straight line. Also, the force experienced by the component perpendicular to `vecB` moves the particle in a circular path. The combined effect of both the components will move the particle in a helical path.