Electric Charge in a Magnetic Field

1. Compensating for Earth's Magnetic Field

1. Note that there are two independent circuits in this experiment:
   1. Supply current to the coils that create the magnetic field ( Figure 2). The current is set by a rotary dial, and the circuit includes a digital ammeter that allows the current to be measured. A double-pole double-throw switch is used to reverse the direction of the current supplied to the coils, which reverses the magnetic field.
   2. The second circuit ( Figure 3) runs the electron tube. There is a high-voltage supply, which sets the accelerating voltage and an alternating signal of 6.3 V connected to a filament. Electrons are, in some sense, boiled off the filament and then accelerated by the accelerating voltage.
2. In the second circuit, turn on the high-voltage power supply to turn on the filament. The light that switches on inside the tube is the glowing filament.
3. Gradually turn up the high voltage to about 2,000 V. The part of the screen inside the tube, which is being hit by the electron beam, should glow blue, making the electron beam visible.
   1. Note that this does not mean electrons are blue - the coating on the screen is phosphorescent and gives off a blue glow when the atoms of this coating are energized by the electrons.
4. Adjust the current through the coils, which create the uniform magnetic field. As the current is adjusted up or down, the path of the beam changes. Adjust the current to pass the beam through a particular (X, Y) point on the grid. Make note of the magnitude of the current required to have the beam pass through that point.
5. Reverse the current to curve the beam in the opposite direction, and adjust the current until the beam passes through the point (X, −Y) (the mirror image of the original point). Again, make note of the magnitude of the current required to have the beam pass through that particular point.
6. Check to see if the magnitudes of the two currents are different. Unless the tube happens to be aligned so the electron beam is parallel to Earth's magnetic field, the Earth's field adds to the field of the coils when the current is in one direction and subtracts from it when the current is in the other direction.
7. Throughout the experiment, average the magnitudes of the two currents, the current required to have the beam pass through a particular (X, Y) point on the grid, and the current required to pass through the mirror-image point (X, −Y), to remove the effect of Earth's magnetic field.

Figure 2: Circuit diagram for the Helmholtz coils. The strength of the magnetic field created by the Helmholtz coils is proportional to the current passing through them. The current supplied to the coils by the adjustable power supply is measured by the digital ammeter. The purpose of the double switch is to easily reverse the direction of the current passing through the coils, which reverses the direction of the magnetic field. Note that the two connections to each coil are marked A and Z, and the two Z's should be connected together to ensure that the coils are producing magnetic fields in the same direction, and not in opposite directions.

Figure 3: Circuit diagram for running the electron tube. The glowing filament that is the source of the electrons is run by a 6.3 V alternating current source. Note that the negative side of the high voltage signal is also connected to one side of the filament, while the positive high voltage signal (on the order of 2,000-3,000 V DC) is connected to an electrode on the right side of the acceleration zone. This produces a large electric field directed left in the acceleration zone, accelerating the electrons from left to right.

2. Data Collection for a Particular (X, Y) and (X, − Y) Combination

1. Note that the tubes are expensive and somewhat fragile. Do not exceed 3,500 V for the accelerating voltage, and turn the accelerating voltage down to zero when measurements are not being taken.
2. In this part of the experiment, record five sets of data, each with a different accelerating voltage with the same (X, Y) and (X, −Y) combination.
3. Note that as the accelerating voltage increases and the electrons travel faster, they do not bend as much, and thus, the magnetic field from the coils needs to be increased to have the beam pass through the same point on the screen. Choose a particular (X, Y) and (X, −Y) point to use for this part of the experiment. Use Equation 10 to calculate the corresponding radius of the beam's path.
4. For a particular accelerating voltage, record the magnitude of the current needed to have the beam pass through the chosen (X, Y) point. Reverse the current, and record the magnitude of the current needed to have the beam pass through the mirror-image point (X, −Y).
5. Average the two currents to remove the influence of Earth's magnetic field.
6. Use the average current in Equation 8 to calculate the strength of the magnetic field.
7. Use the values of the accelerating voltage, radius, and magnetic field to calculate the magnitude of the charge-to-mass ratio of the electron.
8. Choose a new accelerating voltage, and repeat steps 2.3-2.7. Continue to do this until five sets of data have been collected.
9. Compute the magnitude of the average charge-to-mass ratio for the electron.

3. Data Collection for a Particular Accelerating Voltage

1. Collect five more data sets. This time, keep the accelerating voltage constant and change the (X, Y) and (X, −Y) points that the beam passes through. Record the data.
2. Compute the magnitude of the average charge-to-mass ratio for the electron.
3. Average the two average charge-to-mass ratios determined from Section 2 and 3, and state possible sources of error in the experiment.