Question

Write the expression for the force F acting on a particle of mass m &

charge q moving with velocity v in a magnetic field B . Under what conditions

will it move in (i) a circular path & (ii) a helical path?​

Answer 1

Explanation:

Force acting on the particle,F = Bqv. In vector form, F = q (v × B) where, B is uniform magnetic field, v is velocity with particle which is moving. From this equation, it is clear that direction of force is perpendicular to the plane containing both v and B . In other words, force acts perpendicular to both v and B. When velocity becomes perpendicular to force, the path of the object becomes circular.

In this case, B is assumed to act perpendicular to v. In case, B is not perpendicular to v, a component of v remains perpendicular to v. It creates circular path. The component of v parallel to B will create linear path. Here, circular path is due to v cos θ and linear path is due to v sinθ. Both when combined gives helical path.