You can bend a beam of electrons with an applied magnetic field to make a great demonstration of the Lorentz Force.


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Teachable Topics:


Theory:

Recall from your study of introductory mechanics that when a particle moves along a circular path it is constantly accelerating, and there must be a centripetal force producing this acceleration. This force is given by the following equation:

F= mv2/r

Where m is the particle's mass, v is its speed, and r is the radius of its circular path. By applying a magnetic field of strength B perpendicular to the velocity of the moving electrons, we will produce a centripetal force of strength

F = evB

Where e is the charge of a single electron. By combining the two equations above, we get the following expression for the charge over mass ratio of the electron.

e/m = v/Br

In this experiment, the electrons will be injected into the magnetic field by first accelerating them through a potential difference V. Assuming the electron is at rest when it enters the accelerating region, the electric potential energy when the electron enters the region must equal the kinetic energy when the electron leaves the region. In other words,

eV = 1/2 mv2

Putting this equation into the one previous to it yields the following expression which gives the e/m ratio in terms of the accelerating voltage and the applied magnetic field and the radius of circulating electron's path:

 e/m = 2V/B2r2

The magnetic field and the accelerating potential can be manipulated independently, while the radius of the beam's path depends on both V and B. By thoughful experimentation, you can determine the e/m ratio.


Apparatus:


Procedure:

You can use the magnetic field to bend the beam to a specific radius (one of the concentric circles in the vacuum tube). You'll know the beam is hitting one of the radius' because you'll see a green glow from the phosphorescent coating on the lines

Electrons in Magnetic Field

SAFETY WARNINGS!