LEAI-45 Apparatus for DeterminingSpecific Charge of Electron-Basic

Instruction Manual

Lambda Scientific Systems, Inc

14055 SW 142nd Avenue, Suite 22, Miami, FL 33186, USA Phone: (305) 252-3838; Fax: (305) 517-3739

E-mail: s a l e s @ l a m bd a s y s . c o m ; Web: w w w . l a m bd a s y s . c o m

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COMPANY PROFILE

Lambda Scientific Systems, Inc. specializes in developing and marketing scientific

instruments and laboratory apparatus that are designed and manufactured specifically for

experimental education in physics at colleges and universities.

We supply high-quality, reliable, easy-to-use, and affordable scientific instruments and

laboratory apparatus to college educators and students for their teaching and learning of both

fundamental and advanced physics principles through hands-on experiments and

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CONTENTS

1. Introduction ................................................................................................................................ 1

2. Technical specifications ............................................................................................................. 1

3. Working principle ...................................................................................................................... 1

4. Panel controls ............................................................................................................................. 4

5. Experiment Procedures .............................................................................................................. 5

6. Maintenance ............................................................................................................................... 6

7. Accessories ................................................................................................................................. 6

1) Max. input power: 85 W2) Acceleration voltage: 1000 V ~ 1200 V continuously adjustable3) Low voltage DC power:

Current range: 0.2 A ~ 1.5 A/1.5 A ~ 2.5 A continuously adjustableCurrent direction: reversible

4) Parameter of helix tube:Turn number N: 3800 turns/m (unit length of the helix tube)

5) Parameters of oscilloscope tubeDistance: 0.148 m (between screen to y deflection plate 1)

6) Continuous working time: 1 h7) Environmental conditions:

Temperature: -10 to 40 °CRelative humidity: max. 85% (at 40 °C)

8) Dimensions: 380 × 190 × 320 mm9) Weight: 11 kg

Working principle

1

1. Introduction

Electron charge/mass ratio is one of the important constants in modern physics. LEAI-45 adopts the longitudinal magnetic field focusing method to measure the e/m of an electron with an accuracy of better than 5%. Hence it is suitable for experimental demonstration in colleges and universities.

2. Technical specifications

3.

After switching on, the electron in the oscilloscope tube will be subject to Lorentz force under the uniform magnetic field generated by the coil. The Lorentz force can be expressed as:

r s rF = eν × B (1)

where F is the Lorentz force exerted on the electron, ν is the velocity of electron movement,B is the magnetic induction strength, and e is the electron charge.

The direction of Lorentz force is decided by left hand rule and its magnitude is:F = eν B sin α (2)

If the electron’s moving direction coincides with the field direction, then a=0, sina=0. The force exerted on the electron is also zero, and thus the electron will keep its uniform rectilinear movement along its original directions.

When the electron velocity ν is vertical to B (electron velocity is expressed as ν ↑

),

a=90°, sina=1. At that time, the force exerted on the electron becomes F=evB. This force changes electron’s moving direction, but it doesn’t change the magnitude of the electron velocity, and thus the electron makes a uniform circular movement with a radius R in the plane vertical to B, as shown in Fig, 1 (a).

ν

2

Figure 1From Newton’s law, we get:

mν 2

Here, m is the mass of an electron.

F = eν B = ↑ ↑ R

(3)

Thus, the time necessary for an electron to rotate for one revolution is:

T = 2πR

= 2π m (4)

↑ eB

Equation (4) shows that period T is independent of electron velocity, which means, under a uniform magnetic field, the time of rotation of one revolution for electrons with different velocities is identical, except that the higher the electron velocity, the larger the rotation radius of the electron. This is actually the theoretical basis for the magnetic focusing method.

If there is an angle a between electron velocity ν and magnetic field B, the electron velocitycan be decomposed into two components: axial velocity ν // parallel with B; radial velocity ν

↑

vertical to B. ν // remains constant, i.e. the electron will uniformly move along the axis; while

under Lorentz force, ν ↑

will make the electron rotate around the axis. The resulted orbit of movement is a helix as shown in Fig. 1-(b), and the pitch (the travel of the electron in B direction between revolutions) is:

From equation (5), we get:

h = Tν // = 2π m

νeB

// (5)

e =

2π ν (6)

Here, h is the pitch.m Bh

//

If the electrons in an electron beam emitted from the same point have different ν ↑

but

identical ν // , then after travelling a distance h, they will be focused at a point. This is called

magnetic field focusing (i.e. longitudinal magnetic field focusing).

//

3

The electrons emitted from a cathode can be approximately assumed to have no initial velocity. They will be accelerated under the voltage of the first anode (focusing electrode) and secondanode (accelerating electrode) in the tube. The longitudinal velocity of electron ν //

depends on

voltage U (referred to as acceleration voltage) applied by the cathode to the second anode, i.e.1

mν2

2 = eU . Here, e is electron charge, and U is acceleration voltage (the voltage between

the cathode and the second anode).Hence, we get:

ν // =2 e U

m(7)

Substituting equation (7) into equation (6), we get:

e 8π 2U= (8)

m h 2 B 2

The oscilloscope tube is placed with the long helix tube. After switching on, all the electron rays will be focused into a point under the focusing voltage, thereby a bright spot will be found on the screen. To create velocityν

↑ , 15 VAC is applied to a pair of deflection

plates of the oscilloscope tube and the electrons will get a vertical component velocity within a certain range and thus a scanning straight line is formed on the screen.

If current I runs through the helix tube, a magnetic induction strength will be generated in the direction of this helix tube. Under the magnetic field, electrons will make a helix movement, Itis apparent from Equation (5) that ν // (also acceleration voltage U) varies with I (magnitude ofB) in the helix tube, in such a way that h (pitch) is just equal to the distance (l) between the starting deflecting point of the y deflection plate and the center of the screen. In such case, a bright spot shown on the screen is called primary focusing (see Fig 2) and then equation (8) can be rewritten as:

e 8π 2U=

m l 2 B 2 (l ≈ 0.148 m) (9)

Figure 2

2

0

4

Strictly speaking, the magnetic field in a helix tube should be calculated based on field formula for a multi-layer wound helix tube. However, it can be simplified based on thin helix tube formula: B=µ 0NI(cosβ1-cosβ2)/2, as seen in Fig.3.

Figure 3

At the center of the helix tube, B=µ 0NIcosβ. Hence, the equation of e/m ratio is:

e =

8π U =

U × 1014 C / kg (10)

m l 2 µ 2 N 2 I 2 cos 2

β2l 2 N 2 I 2 cos 2 β

where N: turn number of unit length (turns/m) (for this apparatus N=3800 turns/m), µ 0: the magnetic conductivity in vacuum (µ 0=4π×10-7 H/m), I: the current in helix tube, l: the distance between screen and y deflection plate, U: acceleration voltage, and cosβ=0.948.

4. Panel controls

1) Power switch (S1) and indicator (LED)

After switching on S1, the indicator (LED) turns green indicating the power is on.

2) High voltage DC power

a. Brightness adjusting knob (RP1)It is used to control the brightness of electron traces on screen. Warning: never use highbrightness as it may damage the fluorescent materials.

b. Focusing adjusting knob(RP2)It is used to focus electron traces on the screen. Electron traces should be focused whena change in brightness or acceleration voltage

occurs. c. Acceleration voltage adjusting knob (RP3)It is used to adjust the acceleration voltage between the second anode (A1) and the firstanode (K). The acceleration voltage can be read out from the DC voltmeter on the panel.To get a more accurate reading of the acceleration voltage, an external voltmeter with arange of 1500 V can be used by plugging to the red and black terminals marked “high voltage monitoring” on the front panel. Warning: avoid high-voltage shocks.

3) Low voltage power

a. Low power switch (S2)

5

After switching on S2, low DC power will be turned on.

b. Fuse holder for low voltage power

6

This fuse holder holds low-voltage fuses

(3A). c. Current direction (POLARITY) switch

(S4)It is used to change the direction of magnetic field in helix tube during experiment.

d. Current change-over switch (S3)It is used to set the current range at 0.2 A ~ 1.5 A or 1.5 A ~ 2.5 A.

e. Current gain knob (RP4)It is used to control the current running through helix tube. The current can be read outfrom DC ammeter. To get a more accurate reading of the current, an external ammeterwith a range of 3 A can be used. First, remove the short-circuited copper plate between the red and black terminals marked “current monitoring” on the front panel; then the external ammeter should be connected in series with the terminals.

5. Experimental Procedures

1) Turn the brightness knob counter-clockwise to the end, set low voltage switch (LV Source) at “off” position, and turn on power. The indicator should turn green and preheat the apparatus for 5 minutes. A bright strip of roughly 3 cm in length will show on the screen. Now turn the brightness knob to set proper brightness (do not set high brightness!).

2) Adjust the acceleration voltage to 1000 ~ 1100 V while adjusting the focusing knob to focus the bright strip.

3) Turn the current gain knob counter-clockwise to the end, set the current change-over switch at “1.5 A” range, and turn the low voltage power on. Now, the helix tube is energized and the bright strip on the screen will rotate by an angle and shorten.

4) Turn the current gain knob slowly in clockwise directly to increase the current through the helix tube while monitoring the current reading on the ammeter. The bright strip will continuously turn and shorten, it becomes a spot when the current increases to 1 A, indicating that electrons undertake both circular movement and linear movement in B direction, and are focused to a point after traveling a distance of h (l). The readings now are called current I1, and acceleration voltage U.

5) Turn the current gain knob counter-clockwise to the end, and set the current change- over switch at “2.5 A” range. Now the bright spot on the screen will lengthen. Turn the current gain knob slowly to increase the current and the bright strip will shorten. When the current is increased to about 2 A, the bright strip will shorten into a spot. This is the secondary focusing point with the current called I2. A mean current value as I=(I1+I2)/3 may be used in equation (10) to calculate the value of e/m, and calculate experimentalerror of e/m value (well-known value of e/m=1.759×1011 C/kg). Note, the currentdirection is set by the current POLARITY switch. The experimental effect may be some differences for the two directions. Use the direction of having better effect for the acquisition of the experimental data.

7

6) Press the current POLARITY switch to another direction, repeat the above procedures, and observe the bright strip changes (now the current through the helix tube is reversed and the turning direction of the bright strip on screen is also reversed).

7) To calculate e/m value more accurately, external voltmeter and ammeter should be used in connection with the terminals on the front panel. Warning: avoid high-voltage shocks from the terminals marked “high voltage monitoring” on the front panel.

8

6. Maintenance

1) To extend the lifetime of the oscilloscope tube, do not set or use the apparatus under high brightness mode. Before and after use, ensure that the brightness knob is turned counter-clockwise to the end.

2) If the indicator fails to turn on after power-on, pull the fuse drawer located under the apparatus to check and replace the fuse (BGXP-0.75A).

3) If there is no low voltage power after power-on, pull the fuse drawer located under the apparatus to check and replace the low voltage fuse (BGXP-3A).

4) If not in use, the apparatus should be energized every three months.5) The apparatus should be stored in a dry and well-ventilated area, and should be

handled with care.

6) The apparatus should be powered off before movement, wiping, or replacement of fuses.

7. Accessories

1) Power wire, 1 pc2) BGXP-0.75A fuse, 1 pc

3) BGXP-3A fuse, 1 pc

Lambda Scientific Systems, Inc will take no liability for any injury or damage that may be caused by improper handling and/or incorrect operation of this apparatus. Lambda Scientific Systems, Inc assumes no

responsibility for the accuracy and/or the suitability of the information provided in this manual.