Answer to Question #6463 Submitted to "Ask the Experts"

The short answer is that magnetic fields cause beta particles to change direction as the particles cross the magnetic field. The longer answer may be more useful. I do not know what your level of training in mathematics or physics is, but I will try to present a brief discussion that will summarize pertinent aspects of both. I will also try to explain what the end result is in a way that you can follow even if you don't get the details.

Any charged particle moving through a magnetic field (in any direction except parallel to the magnetic field lines) will experience a force. The force will be perpendicular to the directions of both the magnetic field and the velocity of the charged particle. Mathematically we write this as:

F = qv x B,

where F is the force in newtons, q is the particle charge in coulombs, v is the particle velocity in meters/second, and B is the magnetic field in newtons per ampere-meter. Both v and B are vector quantities (they have both magnitude and direction, and the X between the two implies a certain mathematical vector operation referred to as the vector product or cross product). If θ is the angle between v and B the above equation can be written as:

F = qvB sin θ,

where sin θ is the trigonometric sin function, and v and B simply represent the magnitudes of the velocity and magnetic fields, respectively.

In physics it is common to apply a "right hand rule" to determine the direction of the force, F. The convention is understood to apply to a positively charged particle and states that if you extend your right hand with fingers together and your thumb extended separately and then allow your fingers to curl in a direction that would force the v vector to rotate toward the B vector, then your extended thumb would point in the direction of the force on the particle. This is perhaps best seen on a simple picture as below.

In the sketch, the curved arrow is intended to show the imagined rotation of v into B as the fingers curl in that direction; if you are doing this you will find your thumb pointing toward you out of the plane of the paper (or video screen), which means that the positively charged particle would be experiencing a force that is directed similarly. This also means that the particle will then move in the direction of the force. If the particle has a negative charge, as does a conventional beta particle, the force will be in the opposite direction from that experienced by the positively charged particle. Thus, in our picture above, the beta particle would experience a force that is in a direction away from you through the plane of the paper or screen.

When the magnetic field remains constant, and no other forces act on the particle, it will continue to experience this constant force perpendicular to the velocity vector. This forces the particle to continuously change direction and follow a circular path at constant velocity in the magnetic field. This is the fundamental principle that applies in machines such as cyclotrons in which magnetic fields are used to confine the moving charged particle to a circular path. In the case of a conventional cyclotron the circular path increases in radius as the particle receives additional energy from an independent source of radiofrequency input. The principle has also been applied to determination of beta particle energies by sending beta particles in a fixed direction through a magnetic field; the particles are separated from each other according to their energies since they experience different degrees of deflection, the extent of the deflection being related to the particle energy.

You can read more about the details of the motion of charged particles in magnetic fields in most introductory college physics textbooks. Good luck.

George Chabot, PhD, CHP