Moving Electric Charge in a Magnetic Field; Lorentz Force

Figure 1

In this demonstration, a filament produces an electron beam that is deflected by a small plate. Two Helmholtz coils are used to create a magnetic field that bends the electron beam into a spiral pattern, governed by the Lorentz force (figure 1).

Materials:

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Figure 2

  • Teltron tube apparatus with two Helmholtz coils (figure 2)
  • Power supply with 200 V maximum voltage and up to 25 mA current
  • BK precision power supply
  • Six banana cables

Demo:

Connect BK precision power supply to the Helmholtz coils with banana cable. Connect the 200 V maximum power supply B+ terminal to the Teltron tube terminal labeled “electrodes” indicating the deflection plate. Connect the 6.3 V terminal on the 200 V maximum power supply to the terminal labeled “heater”, indicating the filament (See figure 2)

Turn on the 200 V max power supply to “standby” mode; this will begin to run the heater. After one minute, the filament should begin to glow orange. If it does not glow orange, the Teltron tube may be loose; try checking the connection.

Now, test the B+ output (electrodes) to see if an electron beam forms by turning the power supply knob from “standby” to “on”, making sure to keep the voltage below 200 V so not to burn out the filament.

Turn on the BK power supply and run about 0-5 A of current through the Helmholtz coils. A circular pattern should show. You may adjust the current to change the diameter of the circle, and can rotate the ray tube to create a spiral.

Explanation:

The Lorentz force describes the force on a charge moving through an electromagnetic field. As an electron moves through an electric field E and magnetic field B with velocity vector v, a force F is applied to the electron, as shown in figure 3.

F = q(E + B×v)

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Figure 3 – A beam of electrons travelling through a magnetic field, B, pointing out of the page. As the electrons pass though the point x = 0 their trajectory is bent in the + y direction by the magnetic field.

In this demonstration, we use a Teltron tube filled with low density Helium gas. The Teltron tube consists of a filament nestled in a hollow metal cylinder or thimble, which produces electrons as it is heated by the filament. The electrons are ejected, mostly blocked by a metal plate, however a small slot allows a beam of electrons to pass through (See figure 4). The electrons will move in a straight line if there is no external magnetic field.

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Figure 4 – The Teltron tube with no magnetic field.

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Figure 5 – The Teltron tube with a magnetic field pointing into the page due to the Helmholtz coils.

Now let’s turn on the Helmholtz coils. As the beam of electrons moves through the magnetic field produced by the Helmholtz coils, they are bent into a circular motion in a direction both perpendicular to the direction of motion and the magnetic field. In this case, there is no external electric field, the Lorentz force equation simplifies to

F = q(B×v)

In addition, v and B are perpendicular, so the magnitude of the force simplifies to

F = qBv

 As the direction of the electrons’ motion is changed by the magnetic field, the Lorentz force continues to apply force in the direction perpendicular to velocity of the electron and the magnetic field, creating a circular motion as demonstrated in figure 5.

Notes:

Please do not leave the Teltron tube on for more than 30 seconds, as it is easy to burn out. Again, do not let the power supply voltage exceed 200 V.