# sample-lab-report by nuhman10

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```									                    Sample Laboratory Report

There is no set length for a problem report but experience
shows that good reports are typically three pages long. Graphs
and tables make up additional pages. Complete reports will
include the terminology and the mathematics relevant to the
problem at hand. Your report should be a clear, concise,
logical, and honest interpretation of your experience. You will
be graded based on how well you demonstrate your
understanding      of    the    physics.    Because    technical
communication is so important, neatness, and correct grammar

It starts on next page!!!!
Statement of the problem

The problem was to determine the deflection of an electric beam (in x and y
directions) using the screen of a cathode ray tube (CRT) at various potential
differences. We connected the CRT as shown in Appendix D of the lab manual
[1] and recorded the x-deflection and y-deflection resulting from several different
voltages applied to the deflection plates of a capacitor.

Prediction.

The CRT scheme is illustrated in Fig. 1.

L                                           Screen
- - - - - - - - - - - - -
D
Vacc

x                           y1   s
y
E

+ + + + + + + + + + +
y2
Electron with vector acceleration
e=charge of the electron
m=mass of the electron
Path if there were no electric field

Parabolic path due to the electric field E

Straight path (neglecting gravitational force)
Fig. 1

The total deflection of the electron beam is caused by two distinct regions of the
CRT. The first part of the deflection is caused by the electric field between the
plates; the second part is caused by the straight line path after the electron leaves
the plates until it hits the screen. That is,

1 EL  L       1 L L        
ytotal                D          D V y                Eq. 1
2 Vacc  2     2 sVacc  2   
Vy
Where we used the fact that the electric field is found from E       , where s is
s
the separation of the plates in the capacitor and Vy is the voltage applied to it.

deflection (ytotal)

Vy

Data and results

After hooking up the CRT, we turned it on and arranged the screen so that an x-
deflecting voltage would move the beam along the horizontal axis and a y-
deflecting voltage would move the beam along the vertical axis. With no
deflecting voltage, the electron beam did not hit the screen directly in the center -
- we took this point to be our reference point and measured our change in the x-
and y-directions from it.
With some of the variables given in the laboratory manual (See Fig. 2), we could
calculate the distance Dx-Dy after taking our measurements.
6.3 V ACVy DSVx LelectronbeamElectron guntot DVaccDeflection plates

Fig.2
We measured the x-deflection for 6 voltages between 0 and 5 Volts. We then did
the same for the y-deflection. (See table 1)

The largest uncertainty in our measurements came from the deflection of the
electron beam from the screen on the CRT. Since the marks on the screen were
every 1.0 mm and the electron beam was somewhat distorted, we estimated the
uncertainty of our deflection measurements to be 0.5 mm. We verified this
uncertainty measurement by having each member of our group measure the x-
and y-position of the electron beam at two test points. All measurements were
within the stated uncertainty. The uncertainties in our measurement also lead to
uncertainties in the slopes of the deflection vs. potential difference graph; the
slopes were found to have uncertainties of 0.09 mm/V for x and 0.08 mm/V for
y.

Using the values given in the manual, and those found from the experiment, we
calculated the distance between the x and y deflection plates to be 36 mm with an
uncertainty of 12mm.

When we graphed the results from our data table (See Table 1), we saw that the
y-deflection plates gave us a larger deflection at each deflection voltage used in
the experiment. (See Graph 1)

Data:
Predicted deflection
Voltage V ± .05 V Deflection y ± 0.05 cm                          % Error
(Eq. 1)
0.00                0.000
0.50                0.050
1.00                0.112
1.50                0.158
2.00                0.224
2.50                0.269
3.00                0.316
3.50                0.381
4.00                0.474
4.50                0.522
5.00                0.585
from App D
D =7.4 cm
L =2 cm
S =0.3 cm
V =250 V

m =0.112 gr
Table 1
e      deflection
0.00         0.000                                        Deflection as a function of Voltage
0.50         0.050
1.00         0.112                            0.600
1.50         0.158                                              deflection             y = 0.1156V - 0.0094
2.00         0.224                                              Linear (deflection)
2.50         0.269                            0.500
3.00         0.316
3.50         0.381
4.00         0.474                            0.400
Deflection (cm)

4.50         0.522
5.00         0.585
rom    App D                                  0.300
D=     7.4
L=     2
S=     0.3                                    0.200
V=     250

m = 0.112                                     0.100

0.000
0.00        1.00          2.00           3.00    4.00      5.00
Volts

Graph. 1

Conclusions
The result of our experiment is consistent with the dimensions of the CRT. The
total length from the accelerating voltage plates to the screen is 96mm, and our
result showed that the distance between the x and y deflecting plates is
somewhere in the range of 24mm to 48mm. The upper bound value may be
unlikely, since it will not leave much room for anything else to fit in the CRT.
However, this does not mean that the range is unreasonable; any value in the
range can still be made to fit inside the CRT. After discussing this as a group we
realized that we had over estimated the x- and y-position measurements, and the
upper bound value is the result of this.

When we thought about the situation more carefully, we realized that we were
correct in thinking that an electron is always traveling with the same velocity
parallel to the CRT and that the time it is inside each deflection plate will be the
same. Thus, at the far edge of each deflecting plate the electron beam has the
same perpendicular velocity. Recalling our kinematics from last semester, we
realized that this perpendicular velocity will be independent of the parallel
velocity. Since the electron beam takes longer to travel from the far edge of the
y-deflecting plates (the y-plates are further from the screen) than from the x-
deflecting plates, the electron beam under y-deflection will have more time
during which it has a y-velocity, and thus it will be deflected more. This allowed
us to make the right assumptions and thus yielded a reasonable result.

Apendix [2]

First the electrons are given a potential energy by the accelerating potential Vacc
which is converted into kinetic energy, i.e.,
1             2eVacc
U  eVacc        mv2  v 2 
2               m
then, in the E field region, they acted by an electric force whose magnitude is
eE
F  ma  eE  a 
m
1        1
From kinematics:                  y1  y0  v yot  a yt 2  at 2
2        2
L      L
where the time is given by the relationship vx  v                          t 
t      v

Note that the component of the electron’s velocity perpendicular to the field, vx,
remains unchanged by the electric field. Therefore
2
, y1  EL
2
1 2 1 eE  L    eEL2      eEL2     EL2
y1      at                         
2      2 m v   2mv 2
2eVacc 4Vacc           4Vacc
2m
m
D
After the E field region, the electrons take a time t2 to reach the screen t2 
v
and their velocity after the E field region in the y-direction becomes constant and
eE L                                eEL D eELD      eELD
is     given      by    v y 2  at         .   Then     y2  v y 2t 2              2
          ,
m v                                  mv v   mv       2eVacc
m
m
. Therefore the total deflection is y1  y2  EL  ELD  1 EL  L  D 
2
ELD
y2                                                                                 
2Vacc                                                         4Vacc    2Vacc      2 Vacc  2   

1 EL  L    
ytotal                 D
2 Vacc  2  

eL  L     
U  eVacc
1
 mv2  v 2 
2eVacc                ytotal             D Vy
2              m
,                          msv 2  2   
1                  2qVacc
qVacc               
me II  II            (II is the horizontal velocity of the electrons)
2

2                   me

Time in and vertical velocity due to the deflection plates:
L                          qE       qV
tin                  a tin       tin       tin
 II                        me        sme

(s is the separation distance between the 2 parallel deflection plates)

References:

Sources:

[1] Serway, Raymond A., and Jewett Jr., John W. Principles of Physics, Chapter 19

“Electric Forces and Electric Fields”, Thomson Learning, 2002.

[2] Heller, Ken. Physics for Biology and Pre-medicine Laboratory - Electricity,

Magnetism, and Optics. Thomson, 2007, 2008.

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