CHARGED PARTICLES IN A MAGNETIC FIELD
	Measurement of e/m for the electron (Leybold-LaPine apparatus)


PURPOSE:		The purpose of the experiment is (1) to study the motion of charged particles in a magnetic field 
as a function of field intensity and of particle velocity, and (2) to measure the charge/mass ratio for the electron.

APPARATUS:	 The Leybold-LaPine gas-focused cathode ray tube apparatus is shown in the picture below.  
The apparatus consists of a spherical glass bulb, filled with hydrogen at a fairly low pressure.  An electron gun 
inside the bulb produces a beam of electrons, whose path is made visible by a pale blue glow from hydrogen ions 
excited by the electron beam.  The presence of the hydrogen ions, with their relatively small mobility, also serves to 
focus the beam by attracting straying electrons back into the beam.  The velocity of the electrons in the beam is 
controlled by controlling the accelerating voltage applied to the electron gun.

A pair of circular coils of wire, called Helmholtz coils, is used to produce a uniform magnetic 
field within the region occupied by the bulb.  This configuration consists of parallel circular 
coils, of equal turns and equal radius, separated by an axial distance equal to the radius.  In this 
apparatus N, the number of turns of each coil is 130, and Ro, the coil radius is 150 mm.  They 
are connected in series to a 6-volt dc source, and can be loaded up to approximately 5 amperes.






























	ELECTRON BEAM TUBE FOR MAGNETIC DEFLECTION





	CPMF-1
(Leybold-LaPine e/m experiment)	

A regulated high voltage dc power supply can be used to provide the accelerating voltage, 
which can be as high as 300 volts.  This same power supply also provides the necessary 6.3-volt 
ac filament voltage for the electron gun.

In order to measure the diameter of the circular path of the electrons in the electron beam tube, 
use is made of the virtual image produced by a plane mirror.  An illuminated centimeter scale 
(see diagram on next page) is viewed by reflection  from the surface of a plane sheet ot 
transparent plastic.  The position of the mirror is adjusted so that the virtual image of the scale is 
inside the beam tube in the plane of the electron beam.  The beam is then viewed through the 
mirror, and a direct measurement made of the beam diameter.  Notice that there is a 2-cm gap in 
the center of the scale.





















			THEORY:		 The velocity of the electrons in the beam depends on the accelerating 
voltage V applied to the electron gun by the relationship:

				1 mv2 = qV,	(1)
				2
where m is the mass of an electron, v is its velocity, and q is its charge.  The velocity is thus 
proportional to the square root of the voltage.
	
The magnitude of the force on the electrons due to the magnetic field B is given by the 
expression:
	
				F = q vB Sin ?	(2)

If the velocity and the field are at right angles to each another, the path is a circle, and the 
centripetal force is simply F = qvB.  Equating the force to the centripetal acceleration times the 
mass, one obtains the expression:

				R = mv	(3)
				       qB

for the radius of the circular path.


	CPMF-2
(Leybold-LaPine e/m experiment)	



The student should eliminate the velocity v by combining equations (1) and (3), to obtain an 
expression for R in terms of the magnetic field B and the accelerating voltage V.

The magnetic field at the center of a Helmholtz coil configuration can be shown to be given by:

				B = ?o (4/5) 3/2Ni/Ro = 8.992 x 10- 7 Ni/Ro, so B = 7.793 x 10- 4 i Tesla,

	where i is the current passing through each coil.

PROCEDURE:	Obtain sufficient data over the range of 75 to 350 volts accelerating voltage and the range of 0.5 
to 5.0 amperes magnetic field current to plot one of two separate families of curves:  (1) R vs. 1/i for various fixed 
values of V; or (2) R vs. sqrt (V) for various fixed values of i.  Determine the charge to mass ratio for the electron 
from your most accurate data, and compare with the accepted value.  From the estimated error in each measurement, 
calculate the error range for your values of e/m.  Either graph should have 5 data points or more.

	If the initial velocity of the electron beam is not at right angles to the magnetic 
field, the component of velocity parallel to the field will be unaffected by the magnetic force, 
and the path of the electrons will be a helix.

As time permits, qualitative experiments on the effects of bar magnets and other sources of 
magnetic fields on the electron beam may be undertaken and discussed in your report.



APPENDIX:

I.	Derivation of formula for e/m  (q = e).

	(a)	Solve Eq (1) for v2:  v2 = 2qV          					(4).
					          m

	(b)	Solve Eq (3) for v, and square it:	v = qBR
							       m

							v2 = q2B2R2			 (5).
							          m2

	(c)	Combine Eq (4) and Eq (5), and solve for q/m:

					v2 = 2qV = q2B2R2
					        m        m2

					      q  =   2V  					(6).
					      m    B2R2

(d)	Rearrange (6) and take the square root:  R = m  2V  = m  2      V             
							        q   B2      q   (7.793 x 15- 4 i)2,

					or		  R = 1.815 x 103   V 1/2		(7)
							          (q/m)1/2       i


	CPMF-3
	(SAMPLE)
II.	Data Table.	Diameter (2R) of circular path for a given accelerating voltage (V) and a given magnet current (i).  
Diameter in  centimeters, Voltage in volts, Current in amperes.


i \ V
75
100
125
175
200
225
250
275
300
350
0.5











1.0











1.5











2.0











2.5











3.0











3.5











4.0











4.5











5.0








 
































	CPMF-4