MOTION OF A CHARGED PARTICLE IN A MAGNETIC FIELD

1. Motion of a charged particle in a magnetic field

If a positively charged particle moves with an initial uniform velocity in a direction perpendicular to a uniform magnetic field, B, it will move in a circle of radius R in a plane at perpendicular to the magnetic field, with a constant speed v. The radius R is given by

R = mv/|q|B

where |q| is the absolute value of the charge on the particle of mass m.


2. The charge to mass ratio for the electron

In 1897, J. J. Thomson determined the charge (e) to mass (m) ratio, e/m for the electron, using an apparatus which applied perpendicular electric and magnetic fields of known magnitude to a beam of electrons.

In the absence of any applied electric and magnetic fields, a beam of electrons (which are negatively charged) will not be deflected, and continue on a straight path, to be detected at point P on the screen. If an electric field is applied, the electrons will be deflected and detected at the point Pe. In the presence of the magnetic field alone, the electrons will be deflected downwards and be detected at the point Pm.

Now, if both fields are switched on, they can be adjusted so that there is no deflection, in other words, the electrons will hit the screen at point P. This occurs when the two fields exert equal and opposite forces on the electrons. Then, it can be shown that

e/m = E2/2VB2

where E and B are the known strengths of the electric and magnetic fields respectively, and V the known potential difference between the charged parallel plates that produce the electric field.

Bear in mind that this experiment does not give individual values for either the mass or the charge on the electron!








Apparatus for determining e/m