Elektrische veldlijnen ombuigen in een homogeen magnetisch veld

Lorentzkracht: zo kun je het laten zien! In de glazen kolf bevindt zich een elektronenkanon. Dit kanon spuwt een straaltje elektronen uit gelijk aan manneke pis. De glazen kolf bevat een gas waar de uitgespuwde elektronen op bosten. Deze elektronen stromen dus door een vaccuum gevuld met een beetje gas. Bij dat botsen ontstaat er paars licht. Op deze manier wordt het elektronenstraaltje zichtbaar.

Nu we beschikken over een zichtbare elektronenstraal, kunnen we met deze straal gaan spelen. Het leuke van deze elektronenstroom is dat ze qua stroomrichting het niet gevangen zit in een stroomdraad. 

Door een magnetisch veld aan te leggen over deze elektronenstraal, kun je de elektronenstraal afbuigen. 

M.b.v. Helmholtz­spoelen is het mogelijk om het ombuigen van elektri­sche veldlijnen in een homogeen magnetisch veld zichtbaar te maken.

Werking :

De Wehneltcilinder (glazen kolf) is gevuld met waterstofgas.

De elektronen komen vrij uit een kokervormige indirekt verhitte kathode en worden versneld in een elektrisch veld, dat aangelegd is tussen deze kathode en een doorboorde kegelvormige anode.

Wanneer de versnelde elektronen waterstofmoleculen treffen worden deze waterstofmoleculen geïoniseerd. Als de gevormde ionen weer recombineren met elektronen zenden ze licht uit. De baan van de elektronen wordt daardoor zichtbaar.

1. Controleer eerst of de Anodespanning 0 is.
2. Richt het elektronencanon recht omhoog.
3. Wacht op het gloeien.
4. Voer de spanning langzaam op tot 50V. De fijne blauwe straal moet nu zichtbaar worden. Bij sommige apparaten kan het tot 4 minuten duren eer de straal zichtbaar is.
5. Voer de spanning op tot zo’n 200V. Volgens een boek Physics IV is 200V het maximaal toegestane maximum, maar voor deze apparatuur lijkt 250V toegestaan. Maar helaas: onze voeding bereikt deze niet omdat deze bij 200V maximaal 3mA kan leveren. Om de spanning verder op te kunnen voeren is dat te weinig. Dus onze voeding beperkt de mogelijkheden.
   
   NB soms valt na een tijdje de spanning plotseling weg.
   Mogelijk komt dit door een zekering in de voedingskast. Om dit te voorkomen, blijf onder 160V!
6. Zodra de straal het glas raakt, zet dan 10-20V DC op de deflecting plates (Ablenkpl.) en observeer de verandering van de straal.
7. Verwissel de connecties van de Ablenkpl.
8. Voer de spanning op tot ±40-50V

Belangrijk:

• Zodra je de straal niet meer observeert, reduceer dan de anodespanning tot 0.
• Mocht de straal erg diffuus zijn bij voltages tussen 150 en 250V, voer dan 6V toe aan de Wehnelt cylinder.

1. sluit magneetspoelen aan op DC voeding en laat de cirkelbaan zien: lorentzkracht levert de benodigde centripetale kracht
2. Kantelen: spoed van de spiraal wordt groter

E. LETBOLD'S HACHFOLGER • KÖLH-BATENTAL GERMANY

BONNER STHASSE SOt • TELEPH. 4716 . TELEX 08-882815 • TELEGR. LEYBOLDVAK

Printed in Germany

LEYBOLD's Fine Beam Tube

This tube is a special type of cathode ray tube developed from the historical "Wehnelt tube". It is used to show the track of a fine electron beam and the behaviour of the latter in electric and mag-netic fields. In particular it is suitable to the quantitative determination of the specific charge of the electrons by deflect-ing the cathode ray in the homogeneous magnetic field produced by a pair of Helmiioltz coils. (Fig. 1)

The tube is filled with hydrogen to a pressure of approximately 10~2 nun Hg. The gas preseure is selected so that the space charge, produced by the cathode ray in the gas volume, bunches the ray.

This gas focusing is possible only within a restricted range of gas pressure, velocity of electrons and density of electron current.

The cathode-ray tube consists of a glass bulb, 175 mm in diameter, which contains an eccentrically located electrode system, made up of the following. (Fig. 2)

• Independently heated cathode (1 and 2)
• Wehnelt cylinder (3)
• Conical anode with semi-cylindrioal screen (4)
• Pair of deflector plates (5 and 6), placed before the anode.

Electrical data:

Cathode voltage: 6.3 V AC or BC.

Anode:               150-250 V DC continously variable

Wehnelt cylinder: 0-6 V DC, positive with respect to the cathode

(all these voltages can be taken from the power supply 522 35A)

Power supply required to produce magnetic field in the Helmholtz coils: approx. 6 V, 0-2 A from a battery.

EXPERIMENTS

A. Deflection of electron beam in magnetic field.

Assembly:

The magnetic field of a permanent magnet changes the direction of the electron beam. The deflection depends on the direction and strength of the magnetic field (the beam is always deflected normally to the direction of the field). (Fig. 4)

The tracks become clearer when using an extended homogeneous field in place of the inhomogeneous fields of permanent magnets. As was shown by H. von Helmholtz (1849), an almost homogeneous field can be produced between two thin ring-shaped coils placed parallel to one another at a distance apart equal to their radius and each carrying the same current in the same direction.

Therefore the baseboard for the fine beam tube carries two coils arranged in such a way that the tube is between them in a homogeneous field. The tube can be turned in its holders; in this way the angle between the electron beam and the direction of the magnetic field vector can be varied.

If the electrons travel in the direction of the field, or in the opposite direction, then they are not affected by the field. But if the direction of the electrons is normal to the direction of the field, they are continuously deflected. The electron beam remains in a plane which is normal to the direction of the field. Because the same deflecting force acts along each element, the electrons are deflected into a circular motion path. Every moment along a circular path is connected with a radial force directed towards the centre:

(where m is the mass of electron)

This force can only be the deflecting force F e v B.

Therefore, the circular path is given by the equation:

This equation contains two assertions which are capable of experimental verification: the radius of the path increases in proportion to the velocity v of the electrons and in inverse proportional to the magnetic flux density B. On the other hand the velocity v is given by the anode potential V_A

Therefore, the radius of curvature of the beam must increase in proportion to the square root of VA. The magnetic flux density B is determined by the current I flowing through the coils:

;  

Where:

• n is the number of turns,
• d the diameter of the coils
• μ₀ is the permeability for vacuüm.

The radius of the path must be inversely proportional to I. The experiment confirms both these assertions.

If the tube is turned so that the electron beam makes an angle with the magnetic field, the beam describes spiral paths. The pitch of this spiral depends upon the angle between the beam and the field; their diameter depends upon the velocity of the electrons and the magnetic flux density the direction of rotation depends upon the direction of the electron beam and of the field vector.

B. Determination of the specific charge e/m.

Assembly:

If the path of the electron beam is initially normal to the direction of the field, then the electrons will follow a circular path. From the equation for centripetal force

The quantity e/m can be calculated as a function of:

• the accelerating voltage V_A
• the radius r of the circle
• the flux density B of the magnetic field

From  we find  

Although some 10' electrons are present in the gas-focused electron beam, these equations which are derived for one electron can be used. The electrons all have the same properties and therefore cannot be distinguished from one another. Hence the property of a single electron can be inferred from the behaviour of the number of electrons.

For a determination of e/m, we must measure

1) the path radius r for a known value of V_A and

2) the flux density of the magnetic field

1) Measurement of the radius of the circle formed by the electrons.

Measurement of the diameter of the circle described by the electron beam is facilitated by means of a mirror, 8" x 11", placed behind the tube (e.g, the mirror for the wave trough). As shown in Fig. 6 a white strip of paper - or a cross - provided

with several marks, is pasted on the mirror. Then the mirror is held in such a way that the observer sees the luminous beam, its image, and corresponding marks on the paper coinciding without parallax. To achieve this, either the anode voltage or the magnetic field is varied.

2) Magnetic flux density B.

The magnetic flux density B can be calculated from the Biot-Savart law by measuring the coil current I, the coil radius d/2 and the number of turns per coil n:

B is measured in

(The magnetic flux density can also be measured in Gauss: )

I in ampères; d in metres;

B can also be determined by measuring the induced voltage in a coil, For this purpose a mirror galvanometer with the flat coil (516 30) must be calibrated in units of Vs.

For instance we take the flat coil of area A = 3.5 x 10^{-3 m2} with n = 100 turns in the place of the gas-focused beam. We find that the ballistic deflection of a mirror galvanometer when switching on and off the current in the Helmholtz coils is 12.3 divisions for 1 A. We know from a previous calibration that the sensitivity of our galvanometer is 21.9 x 10^-6 V per divisions.

For I = 1 A the transient voltage θ is 12.3 x 21,9 x 10^-6 = 0.27 x 10^-3 vs.

From   we find that 

The value for e/m calculated from above values (1.78 x 10¹¹ coulomb/kg) varies only slightly from the correct value e/m = 1.75x10¹¹ coulomb

C. Electrical deflection; mode of action of the cathode ray tube.

Assembly:

The electron beam emerging from a hole In the conical anode passes centrally between two deflecting plates.

When the deflecting plates are connected with each other and with the anode, the electron beam travels between them in a straight line. If a potential is applied across the plates and the centre tap of the voltage supply is connected to the anode, the electron beam is deflected towards the positive plate (Fig. 9).

An alternating potential can be applied across the deflecting plates by connecting the primary coil of the demountable demonstration transformer across a 1000 ohm potentiometer to the main source 110 V A.C.

The centre tap of the secondary coil is connected with the anode of the fine beam tube, and the 2 ends of the secondary coil with the deflecting plates (Fig. 8). The electrons follow the alternating field without inertia. They fan out and draw a luminous line in the glass.

D. Electron optics in a homogeneous magnetic field.

Assembly:

The beam of electrons, having all the same velocity, is bent in a homogeneous magnetic field into a complete circle, If additionally an A.C, voltage is applied between the deflecting plates, the beam changes to the form shown in figure 11. All the electrons are focus-ed at point B.

Point B represents the image of electrons of different directions but having the same velocity. The position of the image changes with the velocity of the electrons, i.e. moves farther away for slower electrons.

The fact that it is possible to focus a beam of electrons of uniform velocity in a homogeneous magnetic field at one point can be used for determination of velocity of cathode rays, leaving a source in different directions. We measure the distance of the image point from the centre of the anode after the electrons have described a half circle, From this distance we can determine the velocity with respect to the energy of the electrons (principle of an electron half circle spectrometer).

This method of measuring the energy of electrons is especially used for beta-particles (see Leaflets DC 537.533,335;b), For these high energy electrons a strong magnetic field is used (electro-magnet). For indication a photographic plate or a counter is necessary.