Motion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons

Transcription

1 n eperiment of the Electron topic Motion of Electrons in Electric nd Mgnetic Fields & Mesurement of the Chrge to Mss Rtio of Electrons Instructor: 梁生 Office: Emil: Purposes 1. To understnd the movement of electrons in electric nd mgnetic fields, to understnd the electric nd mgnetic focus nd deflection;. To lern the eperimentl method of the electric nd mgnetic focus nd deflection; 3. To mesure the chrge to mss rtio of electron. Apprtus Oscillogrphic Tube. Principle Electron hs certin mss nd electric chrge. Affected by the electric nd mgnetic fields, electron will focus or deflect when it moves in the electric or mgnetic field. According to the focusing nd deflection, we cn investigte some chrcters of electron, such s chrge to mss rtio (e/m). Furthermore, the oscillogrphic tube nd 1

2 television re bsed on electron focusing nd deflection. The structure of oscillogrphic tube SJ31 is shown in Fig. 1. Filment Cthode Accelerting nd Anode X Deflection Grid 1 st Anode Y Deflection Fig. 1. SJ31 oscillogrphic tube Brightness tune: Cthode K is metl cylinder covered by oide, which cn emit electrons when heted up. Due to the influence of electric field, electrons move in certin direction which depends on the direction of the electric field. Grid electrode G is cylinder with smll hole on the top, of which electric potentil is lower thn K. So electrons decelerte between K nd G. Therefore, electrons with lower initil velocity will be rejected bck to K, electrons with higher initil velocity cn pss through the hole of G, then move to the screen. We cn control the voltge of G so tht the number of electrons rech screen will be chnged, by which the brightness cn be tuned, ccordingly. Electric focusing: In n oscillogrphic tube, electrons re emitted from the cthode K. Then, electrons re ccelerted by the first node A1 nd move through the hole of G. Due to the potentil difference between G nd A1, there is n electric field. Due to the curvture of the electric field, it cn be utilized just like n opticl lens. The electrons from different points of the surfce of K cn be focused on the front of G, t which there is focus point. The imging of the focus point cn be shown t the screen due to the electric focusing system including the first nd second nodes A1 nd A. The electric focusing system is lso clled electron lens, which is just similr to the conventionl opticl lens.

3 Whether the electrons cn be focused on the screen only depends on the rtio of V A1 to V A, not the bsolute vlue of V A1 or V A. Therefore, the focus of the electron lens cn be tuned by chnging the rtio of V A1 to V A. By choosing the pproprite rtio, the electron cn be focused on the screen. In prcticl ppliction, the second node A is lso clled ccelerting electrode becuse of its function of ccelerting electrons. The first node A1 is clled focus electrode due to tht it is used for chnging the rtio of V A1 to V A. Actully, chnging V A cn lso tune the focus, so, A is lso clled ssistnt focus electrode. Mgnetic focusing: If the ccelerting electrode, the first nd second nodes nd both X nd Y deflection electrodes re connected together to high voltge compred to the cthode, the electrons from the first focus will move with constnt velocity in the zero electric field. The electrons cn not be focused on the second point without the focus electric field. If there is uniform mgnetic field with mgnetic induction intensity of B long the direction from G, electrons re ffected by the Lorentz force, which cn be epressed s: F=-e B (1) The velocity of electrons v could be little different from the is, then, v cn be decomposed into v nd v //. v // pproimtes to be v, nd Lorentz force hve no effect on electrons t this direction. At the verticl direction, electrons re ffected by the force F = ev B. The Lorentz force is verticl to v, so, it is centripetl force. By this centripetl force, electrons move s circulr motion with constnt velocity. Lorentz force is equl to centripetl force nd we cn obtin: v ev B = m () R The rdius of the circulr motion cn be clculted by: mv R = (3) eb The period is independent of velocity, nd cn be epressed s: 3

4 T π R π m = = (4) v eb Electrons move t constnt velocity long the is, besides, they move round the es. As result, their orbit is heli. After period, electrons displcements long the is re the sme. So they will be focused gin t the point s: h=v // T=πm v // /eb (5) where h is the thred pitch of the heli. Every integrl multiple of h is lso the focus. For n pproprite B kh (k is positive integer) is equl to l 0 (the distnce between the first focus nd screen).this is so clled mgnetic focusing. Mesuring chrge to mss rtio: The velocity of electrons depends on the ccelerting voltge U, s hve: 1 mv eu =. Becuse electrons re pril, then, we v // eu v= (6) m When focusing, we cn obtin: l The chrge to mss rtio of electron cn be clculted by: 0 π k mu = kh= (7) B e e m 8π U = k (8) l0 B The mgnetic field of oscillogrphic tube is produced by the solenoid round it. For solenoid with length L, dimeter d, circle number of ech unit length n, eciter current I, the mgnetic induction intensity of the mgnetic field induced t the center cn be epressed s: B= μ ni 0 d L + l (9) 4

5 Electric deflection: There re couple of deflection pltes, verticl Y nd horizontl X. If there is voltge V between the deflection pltes, electrons will turn to node. By DC voltge, we cn see bright spot shown on the screen. By AC voltge, we cn see bright line shown on the screen. It cn be proved tht lrger V leds to longer displcement nd they re with liner reltionship. Proportionlity constnt is equl to the number of displcement under unit deflection voltge. The scle constnt is clled deflection sensitivity S (cm/v). Reciprocl of S is the deflection fctor (V/cm). S nd 1/S t direction of X nd Y cn be epressed s: S = y, Sy V = V (10) y 1 V 1 V y =, = (11) S S y y Mgnetic deflection: When there is mgnetic field which is perpendiculr to is, electrons will deflect by the impct of Lorentz force. The orbit rdius of electrons is R=mv/eB. The deflection ngle θ is quite smll, then, tnθ=b/r=y/l, nd mv /=eu, so, we cn obtin the displcement of the bright point: e y = blb (1) mu There re severl wys to generte the B. For emple, in television, sddle like coil cn be used to generte the uniform mgnetic field. In this eperiment, the Helmholtz coils re hung up to the two sides of the long stright solenoid to generte the mgnetic field. The Helmholtz coils generted mgnetic induction intensity cn be epressed s B=k 0 I. Here I is the mgnetic generting current, k 0 is determined by the circle number nd geometricl prmeters of Helmholtz coil, which is presented by lb. The reltive lrger deflection ngle cn be relized by the mgnetic deflection, which is suitble to the using of huge screen nd is generlly employed for kinescopes. 5

6 However, there re reltive lrger inductnce nd cpcitnce, which is not suitble for high frequency pplictions. Therefore, the electric deflection is usully utilized in oscillogrphic tubes. Procedures (1) Operte nd observe tuning the brightness. () Operte nd observe tuning the electric focusing. (3) Operte nd observe tuning the mgnetic focusing. (4) Mesure the chrge to mss rtio of electron. Estblish the circuit. Choose the vlue of ccelerting voltge U in the rnge of 800~900 V. The brightness will be chnged when tuning the ccelerting voltge. The brightness should not be too high to void dmging screen, in ddition, pproprite brightness is necessry to mke n esier evluting the focusing. Increse the mgnetic generting current from 0 A. Mesure the first focus current I 1 6 times nd clculte the verge vlue. Use I 1 to clculte the chrge to mss rtio. Increse the mgnetic generting current to mesure the second nd third focus current I nd I 3 6 times nd clculte the verge vlue. Clculte the chrge to mss rtio by I nd I 3, respectively. Reverse the current of the solenoid nd repet the opertions described bove. (5) Mesure the deflection sensitivity S nd deflection fctor 1/S. Estblish the circuit. Choose vlue of ccelerting voltge. Mesure the deflection voltge in the cses of the bright line is 1 cm, cm,, 5 cm long, respectively. Clculte S nd 1/S. Mesure them t X nd Y (miml deflection is 4 cm) directions. Elective: Investigte the reltionship between the deflection sensitivity S nd ccelerting voltge U. Eperimentl Prmeters re s follow: distnce between the first focus nd screen l 0 =0.199 m 6

7 length of the coil of solenoid L=0.60 m circle number N=nL=1596 eternl dimeter is m internl dimeter is m The mgnetic induction intensity B cn be clculted by verge dimeter. Bsic Requirements 1. To operte nd observe the electric nd mgnetic focusing.. To Mesure the chrge to mss rtio. 3. To clculte the deflection sensitivity S nd deflection fctor 1/S. Attentions 1. Keep sfety during the eperiment by pying ttention to the high voltge between K nd G, etc. Do not mke short circuit between high voltge nd the ground; Do not feel free to chnge the dynmic rnge of the electricl meters;. The opertion during eperiment should be chieved by ONE HAND, do void touching object connected to the ground by the other hnd; 3. For the focus opertion, keep the screen sfe by void operting too high brightness. Discussions 1. Anlyze the reson tht cuses mesurement errors from instruments nd methods, propose the suggest.. Bsed on the electric deflection, mgnetic field is generted to be verticl to the electric field. Therefore, electrons will be deflected by the impct from both the electric nd mgnetic fields, which is the eperimentl method bsed on orthogonl electric nd mgnetic fields. In 1897, English physicist J. J. Thomson mesured the 7

8 chrge to mss rtio of electron by the eperimentl method described bove in Cvendish lbortory, by which he won the Nobel Prize for Physics in Try to present the formuls nd propose n eperimentl design. Elective Reding: derivtion of the electric deflection The length of deflection pltes is b. The distnce between the two pltes is d. Electrons re deflected due to the force ev/d between the two pltes. The ccelertion of electrons is b =ev/(md), nd the time for pssing b is t b =b/v //. So, the deflection distnce of electrons is b 1 1 ev b = btb = md v//. The X component of the velocity of electrons rriving t the edge of the plte is v = t b b. When leving the pltes there is no electric force ffecting the electron, s result of which, electrons move with constnt velocity t X direction. The time for pssing l is t l =l/v //. Therefore, the deflection distnce t X direction is l evb l = btbtl=. The totl deflection distnce mdv v // // cn be epressed s: When considering 1 // evb 1 = b + l = b+ l mdv mv = eu, we cn get // (13) bl = V (14) du The sitution t Y direction is similr to the nlysis bove, then, we cn obtin: bl = V, du bl y y y = Vy (15) du y 8