Question

1. A beam of charged particles enters a magnetic field and travels in a helical or spiral path What does the shape of the path indicate about the initial velocity of the particles?
A. The initial velocity is parallel to the magnetic field.
B. The initial velocity has components both parallel and perpendicular to the magnetic field.
C. The initial velocity is perpendicular to the magnetic field.
D. The initial velocity has greater magnitude than particles traveling in a circle through the magnetic field.

Answer 1

B. The initial velocity has components both parallel and perpendicular to the magnetic field.

Explanation:

When a charged particle moves in a magnetic field, it experiences a force which is given by

$F=qvB sin \theta$

where

q is the charge

v is the velocity of the particle

B is the strength of the magnetic field

$\theta$ is the angle between the directions of v and B

From this formula, it is clear that the force has only a component in the direction perpendicular to direction of the the motion of the particle. Therefore:

• if the initial velocity is perpendicular to the magnetic field, then the particle will follow a perfectly circular path
• If the initial velocity is parallel to the magnetic field, then the particle will continue moving straight, since it will experience  no force
• If the initial velocity has components both parallel and perpendicular to the magnetic field, then it will move in a helical or spiral path, which is a composition of the two motions above (straight motion + circular motion)