Laboratory for 2/23/98

The ratio of the electron's charge to its mass can be obtained using an electron beam of known KE and a uniform magnetic field. An electron beam is created by accelerating electrons "boiled" from a hot filament (cathode) towards two plates (anode) which is maintained at a potential above the filament. The Leybold fine beam tube consists of such a cathode/anode arrangement enclosed within a glass tube filled with a rarefied gas. The beam can be seen as the gas molecules give off a faint blue light from the collisions with the electrons. A uniform magnetic field, created by two Hemholtz coils, bends the beam into a circle which can be measured.

1. Derive the expression for the e/m ratio
   

   where

   • V = the cathode to anode voltage
   • B = the magnetic field strength
   • r = the radius of curvature of the electron beam

   Help with the derviation can be found in Sec 34-3 of the Phys 242 text (Halliday/Resnick/Krane, 4th ed).

2. Derive the expression for the magnetic field strength
   

   where

   • N = the number turns in each coil (130)
   • I = the current in each coil
   • d = the diameter of each coil (.3 m)
   • ľo = magnetic permeability of free space

   Note that the coils are separated by a distance of d/2.

   Help with the derviation can be found in Sec 35-2 of the Phys 242 text (Halliday/Resnick/Krane, 4th ed).

3. Carefully read the instruction sheet for the fine beam tube instrument and be certain that you have a thorough understanding of its operation and all connections are correct. Incorrect connections can easily destroy the apparatus. The filament is particularly vulnerable.

Measure the coil current necessary to produce a circle of radius of approximately 4 cm for accelerating voltages of 150 V, 200 V, 250 V, and 300 V. Check along several diameters and determine the average. Calculate e/m for each trial and compare with accepted value. Discuss the difficulties with this experiment and the sources of error.