e/m Helical Method

Apparatus

• Electron beam source (e.g., thermionic emission in a vacuum tube)
• Helmholtz coils to generate a uniform magnetic field
• Phosphor-coated screen to visualize electron motion
• Power supply for accelerating potential and coil current
• Measuring tools (calipers, scale, or camera for image analysis)

Apparatus

• Electron beam source (e.g., thermionic emission in a vacuum tube)
• Helmholtz coils to generate a uniform magnetic field
• Phosphor-coated screen to visualize electron motion
• Power supply for accelerating potential and coil current
• Measuring tools (calipers, scale, or camera for image analysis)

Procedure

1. Setup: Arrange the electron beam apparatus within the Helmholtz coils.

2. Apply Magnetic Field: Pass current through the coils to generate a uniform magnetic field.

3. Generate Electron Beam: Accelerate electrons using a known voltage $V$.

4. Observe Helical Motion: Adjust the beam entry angle so that electrons exhibit a helical trajectory.

5. Measure Parameters:

   • Helical radius ($r$) from the screen.
   • Pitch ($p$) from side-view imaging.
   • Magnetic field strength ($B$) from coil current and known coil parameters.
   • Accelerating voltage ($V$) to calculate initial velocity ($v$).

6. Calculate $e/m$ using the relationships:

e/m=2VB2r2e/m = \frac{2V}{B^2 r^2}e/m=B2r22V​

Alternative approaches involve analyzing the pitch $p$ and using time-of-flight techniques.