Interactive Lecture Demonstration 8 – Electron's Charge-to-Mass Ratio

In this demonstration, a beam of electrons inside a partly evacuated glass sphere will enter a magnetic field that is perpendicular to the direction of the electrons' velocity. The magnetic field will be produced by two coils of wire arranged so that the separation of the coils is equal to their radius. This configuration of coils, called Helmholtz coils, produces a nearly constant magnetic field in the region between the coils.

When charged particles move in a constant magnetic field, the particles experience a constant force that is always perpendicular to their velocity. The particles therefore execute circular motion. Since the magnetic force is always perpendicular to the particles' velocity, the force does not do work on the particles, so the particles move at constant speed.

We will use the apparatus to determine the ratio of the electrons' charge to their mass, a fundamental physical quantity. This quantity was first measured in a famous experiment by J. J. Thomson is 1897, using a cathode ray tube and an electric field to deflect the electrons (instead of the magnetic field that we will use).

You will be able to see the electron beam only because the sphere is filled with mercury gas. When the electrons in the beam collide with mercury atoms, they excite the mercury electrons to higher energy orbits in the mercury atom. The mercury electrons then drop back to their original low-energy orbits, emitting blue light in the process.

1. The source of electrons is a filament through which a current passes. An anode (at a high voltage relative to the filament) creates a strong electric field near the filament. The electric field is strong enough to pull electrons out of the filament (this is thermionic emission, the same process by which an electron beam is formed in a cathode ray tube).

Let's assume the electrons are at rest when they leave the filament. If the voltage of the anode is 400 Volts higher than the filament, how fast are the electrons traveling when they reach the anode ?

2. Refer to the diagram above. What direction should the magnetic field be in order to make electrons move in a clockwise circle inside the glass sphere ?

3. What direction (clockwise or counterclockwise) should the current go through the Helmholtz coils in order to produce the necessary magnetic field ?

4. Now we will turn on the current in the coils, producing a magnetic field inside the sphere. We will adjust the current to make a magnetic field strong enough to bend the electrons in a complete circle inside the sphere. Do a net force problem for an electron when it is traveling in a circular path in the constant magnetic field produced by the coils. Solve your net force equation to find q/m, the ratio of the electron's charge to mass, in terms of the radius of the electron's circle, speed of the electron and strength of the magnetic field.

5. The formula for the strength of the magnetic field produced by Helmholtz coils is

B = 8 m₀ N I / a √125

where I is the current through the coils, N is the number of turns of wire in each coil and a is the separation distance of the coils. For our coils, N = 130. Measure the current and the separation distance of the coils, then calculate the magnetic field strength.

6. Now measure the radius of the electrons' circular path. Use your data to calculate the ratio q/m. Compare your result with the accepted value for q/m found in your textbook.