2/11/06 clc 

Electron Charge/Mass Ratio, Hoag Apparatus

Here a modified cathode-ray tube is used to measure e/m for the electron.A beam of electrons is sent down the axis of the tube parallel to a known magnetic field supplied by a solenoid.When the beam is caused to begin its trajectory with some lateral motion, its lateral trajectory will be a circle.Focus of the beam on the tube face occurs when the time for completing the circular path is equal to that for trip down the tube’s axis, and the value of magnetic field needed to obtain this condition provides a measure of e/m.

The apparatus includes:

·              e/m cathode-ray tube

·              Solenoid

·              Tube control circuit

·              2 digital multimeters

·              External resistance box (coarse solenoid current control)

The accelerating and grid voltages are generated in the grid control box.The solenoid current supply, ~100 V D.C., will be provided to your table from a house D.C. generator.

Please handle the tube with care. Measurements of lx and ly are difficult due to the opacity of the tube.Past measurements have yielded ly=15.29 cm and lx=13.21 cm from the back of plates to screen.

            Q.Is the write-up correct in assuming that the entire deflection takes place immediately when the electron enters the deflection region?How would you improve on this assumption?Hint:The electrons follow a roughly parabolic trajectory in the region of the deflection plates.Is this effect a large one?

 

Tips: Be sure the ground cable is connected. Keep the brightness (B) as low as possible.

 
 

 

 

 

 

 


WELCH MANUAL

INSTRUCTIONS FOR THE USE OF

#627 HOAG E/M APPARATUS

Manufactured by

W.M. WELCH MANUFACTURING COMPANY

1515 Sedgwick St., Chicago, IL

THE PRINCIPLE OF OPERATION

The most important part of the apparatus is the special vacuum tube.This is similar to the RCA-906 cathode ray oscillograph tube except that it has been constructed entirely of non-magnetic materials.It may be used in place of a 906 tube in any application.

As used in the experiment to determine the ratio of charge to mass (e/m) of the electron, the narrow beam of electrons produced in the “gun” of the tube passes between the plates of a condenser and continues to a luminescent screen where it produces a small spot of light.An alternating potential applied to the condenser plates deflects the electron beam rapidly back and forth so that a line of light appears on the screen.The tube is also located in a uniform magnetic field in such a manner that the magnetic lines of force are parallel to the axis of the tube.Under these conditions the magnetic field does not effect the forward motion of the electrons since the lines of force are in the same direction as the beam, but it does act upon the perpendicular component of their motion (which was produced by the electrostatic field of the condenser).From the elementary motor rule, one may see the effect is to deflect the electrons into circles in planes at right angles to the tube axis.The circles are larger for the larger electrostatic deflecting potentials and are all tangential to the axis.It can be shown that the time for an electron to rotate at a slow speed in a small circle is the same as for one to rotate rapidly in a large circle; all electrons rotate with the same angular velocity.The result of the combined uniform circular and uniform linear motions is such that the electrons follow helical paths down the tube.

The strength of the magnetic field is varied until the time for the electrons to make one revolution is equal to the time for them to travel forward from the condenser plates to the screen.Then all electrons will again be on the axis and a spot of light will be derived and used to calculate the value of e/m.

The procedure is:first, to focus the electrons on the screen, second, to apply the electrostatic field so as to form a straight line on the screen, third to apply and increase the magnetic field until the line has rotated and shrunk into a small spot of light, fourth, to substitute in the equation for e/m.

MEASUREMENTS ON THE SOLENOID

(1)Measure the length L of the solenoid, in centimeters.This is the distance between the ends of the turns of wire and does not include the end plates.See Figure 1.

(2)Measure the mean radius r of the solenoid, in centimeters.To do so, measure the outside diameter of the wires and also that of the supporting tube.Their sum, divided by 4, is the distance r form the axis to the center of the windings, see Figure 1.Tan  is equal to r divided by L/2 and cos  may be found directly in trigonometric tables.

(3)Record N, the total number of turns of wire on the solenoid.

CONNECTIONS

(1)Arrange the apparatus as in Figure 2 placing the solenoid in a location as free as possible from magnetic objects and stray magnetic fields and at least one and one-half feet from the Control Box and motors.The magnetic fields of the transformers in the Control Box and of the permanent magnets in the meters are thus avoided.

(2)Turn the “Off and On” switch of the Control Box to the “Off” position and the Solenoid switch (lower right) to its “Off” position.

(3)In the rear center of the Control Box, plug in the tube cable and slide the tube in its holder into the rear of the solenoid so that the white screen may be seen from the front.The “center” of the tube should be located at the center of the solenoid as in Figure 1.The “center” of the tube is located behind the screen by a distance equal to the sum of lx and ly divided by 4. This location of the tube may be in error by a centimeter or two without seriously affecting the final result since the magnetic field decreases but slowly along the axis, near the center, of the solenoid (0.3% in 5 cm).

(4)Connect the ground wire provided with the apparatus to the single binding post on the rear of the solenoid.If the metal tube of the solenoid is not grounded, erratic operation of the spot of light will result due to electrostatic charges on the glass walls of the vacuum tube.

(5)Connect wires from the pair of binding posts on the solenoid to the right end terminals of the Control Box, which are marked “To Solenoid.”Polarity is unimportant, as a reversing switch has been provided on the box.

(6)Connect a 0-1000 d.c. millimeter of good quality to the left side terminals, marked  .This serves to measure the current through the solenoid and should cover the range from 0.1 to 0.9 amperes in steps of 0.01 amperes.Accurate values of this current are very essential since they are squared in the final equation and any error in their value will cause twice as large an error in the computed value of e/m.

(7)Connect a 0-1500 d.c. high resistance voltmeter to the left side binding posts marked  .This serves to measure the total voltage used in the acceleration of the electrons.A Weston d.c. 1000 ohms per volt, model 489 meter, reading to 750 volts, has been used satisfactorily in series with a multiplier of equal resistance, i.e., 750,000 ohms.The scale reading is then to be multiplied by two.The resistance unit used as a multiplier must be capable of dissipating sufficient heat, say 10-25 watts, that it does not overheat and change in value during use.Western Electric “lavites” have been found satisfactory but others of equal heat capacity may be used.Calibration may be made, below 750 volts, by comparing readings with and without the multiplier, to see that the added resistance decreases the readings to half value.Accuracy in the voltmeter readings is not as important as in the ammeter readings.

(8)Plug in the 110 volts a.c.The lead wire may be found coming out of the rear of the Control Box, near the tube cable plug.

(9)Connect the 100 d.c. to the binding posts on the right side of the Control Box.The lowest voltage that can be used is about 90 volts.If higher voltages alone is available, such as 220 d.c., add a series resistor to limit the current to 1 ampere.

ADJUSTMENT

            When the apparatus has been properly connected, turn the main switch in the Tube Control section of the Control Box to the “On” position.After about half a minute, a green spot of light should be seen on the screen.If none appears, turn the knobs B and F.As seen in Figure 3, the knob B controls the negative potential of the grid G and hence the number of electrons which can pass out of the gun; in other words, B controls the Brightness of the spot on the screen.It may also be seen in this figure that the knobs F and V control the positive potentials on the two annodes A1 and A2.The sharpness of focus of the electron beam is determined by the ratio of these two potentials, so that F serves (for a fixed value of V) to determine the Focus of the beam on the screen.A change in any of the B, F or V values will alter the remaining values.

The theory used in this method of determining e/m requires that the electrons travel in a parallel beam through the condenser; they must not converge or diverge from the axis until the electrostatic potential is applied to the plates.The “cross-over” image of the cathode is about one-half millimeter in diameter.This, then must be the approximate size of the spot on the screen.

            Set the voltage at a fixed value, say about 1200 volts, by turning the knob V.Now, vary B and F so as to reduce the size of the spot until it is a millimeter or less in diameter and as nearly circular as possible (no tails).The spot will not be intensely brilliant but may be seen without darkening the room.This adjustment is exceedingly important, for if the spot is too large, the electrons will start diverging from the axis somewhere in the gun and the values of lx and ly used in the computations will be smaller than the true values and e/m will come out too large.Conversely, if the spot is too small, e/m values will be too small.Since the exact conditions, which produce a parallel beam can only be stated in terms of the size of the spot on the screen, the student should try various sizes from one millimeter down to the smallest which is visible in the following.

THE EXPERIMENT

(1)With a circular spot of about one-half millimeter diameter, turn the Deflection switch to “X” and vary the X knob until the faint line, which appears on the screen is of maximum length.It will be shorter at the higher voltages.The exact length is not of great importance.

(2)Now turn the “Solenoid” switch to, say the left side and increase the solenoid current, first with the coarse and later with the fine adjustment until the line has been reduced to a small point.This is an exceedingly sharp adjustment and hence can be made with considerable accuracy.When the line has been reduced to a small point the electrons have executed one helical revolution and the equation for e/m (to be given later) may be applied.The voltmeter and ammeter readings, which exist at this instant, are to be used in the equation.The readings must be taken at the exact instant when the electrons from the point, since a delay may give incorrect values due to line voltage fluctuations.

(3)Now reverse the solenoid current (to the right side), readjust for a fine point of light and read the meters.Average the two sets of readings and use in the e/m equation.The averaging process will correct for extraneous magnetic fields such as that of the earth.

(4)Without changing the spot size, use the Y deflection plates as above for the X plates, obtaining an average value of I and V for the reversed solenoid currents.

(5)Repeat (1) – (4) with a slightly larger, and again, with a slightly smaller spot.

(6)Repeat (1) – (5) at several different accelerating voltages, spaced, say 100 volts apart over as wide a range as the apparatus permits.

The data may conveniently be recorded in a table headed by Plate (X or Y), Volts, Amps, Average Volts, Average Amps, and e/m.

CALCULATIONS

It can be shown that, under the condition that the deflected electrons have been rotated by the magnetic field so as to produce a small point of light on the screen, (in MKS units) 

 

e/m = 5 x 1013  (L/Nlx cos q)2 (V/I2)

 

Drive this:

L = Length of solenoid.

N = Total number of turns on solenoid.

lx = Distance from deflection plates to screen (or ly). 

q= The half angle at the center of the solenoid, see Fig. 1.

V = Electron accelerating potential in volts.

I = Current through the solenoid, in amperes, at the instant the fine spot of light has been formed on the screen.  

The “correct” value of e/m is 1.76 x 10^11  C/kg.From this value and the value of e as determined by the oil-drop apparatus (No. 20 of the W.M. Welch Manufacturing Co.), the mass m of the electron may be computed with that of ordinary objects.

ADDITIONAL USES OF THIS APPARATUS

The Control Box and cathode ray tube may be used in the many well-known applications of the cathode ray oscillograph.The three binding posts in the lower center of the front panel of the Control Box have been provided that one may connect any desired external current to the deflecting plates, as, for example, a “sweep circuit” and a current whose wave form is to be studied.The center, or common post, is grounded to the chassis of the box.The “Deflection” switch X-Y MUST BE AT ITS “OFF” POSITION when connecting to external circuits, otherwise the alternating current of the upper transformer in Figure 3 will cause trouble.If on the “X” position, the Y binding posts may be used for comparison of an external current with the alternating current of the supply lines.

The solenoid may also be used in many other experiments, as for example, the measurement of field intensities along the axis of a solenoid.It can stand several amperes, continuous operation, and produce several hundred gausses at its center.The field intensity is about 50 gausses in the e/m experiment.