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# Electric Fields and Electrons’ Deflection

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The cathode ray tube's operation will be studied in the lab. A cathode ray tube is the component of a TV set that creates the image, by definition. Additionally, it aids in making the graph on an oscilloscope. For this reason, the lab serves a crucial role in providing an introduction to the oscilloscope experiments and a comprehension of how the electric fields affect the charges. The electrons that are released from the surface of the cathode in this lab are accelerated by the electric field. This electric field is directed along the tube's long axis, as you can see. The application of a large potential difference between the short distance in front of the system and the cathode provides this field.

The lab has a total of three sets of data with various uncertainties. For example, the uncertainties of “negative” values in dataset I range between ± 0.02 V and ± 0.03 V for all the values of voltages measured. The uncertainty of the “positive” values is ± 0.01 V. Dataset II has an uncertainty of ± 0.01 V. In the first data, a graph of the displacement of spot versus displacement voltage Vd is made. After fitting the straight line through the origin, it was evident the increase in spot displacement causes a rise in the displacement voltage Vd. Accordingly, a graph of the deflection D versus 1/Va was plotted in dataset II. Finally, data set III helped in explaining how to find the Lx and Ly ratio. According to the mathematical analysis, it was established that tan-1 (8/4) = 63.40.

Experimental Procedure

In the first place, a circuit was connected using a 40 V power supply that is linked to the deflection plates of “x-x”. After setting the red power supply to about 250 V, the focus control was used for obtaining a small dot on the face of the tube. Subsequently, the setting on the green power supply was varied to observe what was happening. In the same way, the plastic grid on the tube’s surface was rotated to make the beam move parallel to the grid's "x-x" plates. At this point, the “x-y” grid was drawn in the notebook using the same number of squares. In this way, the position of the spot was quickly recorded by the use of the same approach.

In dataset I, the spot position was registered with zero deflection voltage Vd while keeping the acceleration voltage fixed. Afterward, the spot position was recorded for five “negative” values and five “positive” values of Vd. In dataset II, one of the values of Vd was obtained from the data set I for acting as a voltage of fixed deflection for the set of data. Another picture of the grid was again drawn in the notebook for recording the data. The spot position was marked with Vd set to zero for each of the three more accelerating voltage values.

In dataset III, the same accelerating voltage as in dataset I was used for connecting the green power supply to the tube's "y-y" inputs. Here, what happens was observed and recorded while the Vd was being varied. Consequently, the green supply was connected simultaneously to the power supply’s “x-x” and “y-y” inputs. Further, the angles of the motion of beam spot were measured across the grid as Vd was being varied.

Data

Table 1: Dataset I

Negative

1

0 V

-1.5 mm

0.5 mm

2

-13.5 ± 0.02 V

-11 mm

0.5 mm

3

-19.00 ± 0.03 V

-15 mm

0.5 mm

4

-5.11 ± 0.03 V

-5 mm

0.5 mm

5

-9.18 ± 0.02 V

-8 mm

0.5 mm

Positive

6

9.15 ± 0.01 V

5 mm

0.5 mm

7

16.10 ± 0.01V

10 mm

0.5 mm

8

23.26 ± 0.01 V

15 mm

0.5 mm

9

30.21 ± 0.01 V

20 mm

0.5 mm

10

6.73 ± 0.01 V

3 mm

0.5 mm

Dataset II

Vd = 9.15 ± 0.01 V

(-3 mm, 2 mm) (150V) = Va

(8 mm, 2 mm) (150 V) = Va

(3 mm, 0 mm) (400 V) = Va

(4 mm, 0.5 mm) (325 V) = Va

Vd = 0 V (-5 mm, 0 mm) (400 V) = Va

Table 3: Dataset III

Vd = 0 V

Vd = 9.15 V

Va

(-3,2)

(8,2)

150 V

(-0.5,0)

(3,0)

400 V

(-1,0.5)

(4,0.5)

325 V

Data Analysis

Figure 1: Graph of Displacement Versus 1/Vd (1/V)

Figure 2: Graph of Displacement Versus Vd (V)

The angle of the motion of the beam across the grid as Vd being altered = tan-1 (8/4) = 64.40. Mathematically, the speed of an electron in cathode = ½ mv2 = eV. Where, e = 1.6 x 10-19C, and m denotes the electron’s mass = 9 x 10-31kg (Peter 2). This field causes an electron acceleration of 2eV1/m = Vx2. Notably, l/Vz is the time the electron spends between the plates because their paths become straight line (Findlay 5). Again, this is the time it also takes for traveling the length of the plate. Combining the two equations i.e. 2eV1/m = Vx2 and l/Vz, the result becomes, Vx = eVdl/ (mdvz). However, if the distance between the phosphor screen and the deflecting plates is L, then the electron beam D will impact at (lL/2d) (Vd/Va).

According to the results, the electric field that acts on an electron increases with an increase in the value of Vd. The direction of the deflection also reverses when the Vd polarity is reversed. In the same way, the displacement increases with an increase in the value of 1/Vd. Given that tan = y/D, then Vy/Vx = y/D. Thus, the ratio of Lx to Ly = D:y (Kroemer 11).

Conclusion

Even though there was some uncertainty in the values obtained, this lab succeeded to study the cathode ray tube’s operation. It has been established that the deflection tube of electron enables the possibility of studying electrons deflections in an electric field qualitatively. The deflection of electrons occurs in the two capacitor’s field plates which are built in the tube. In this process, the electrons are evaporated from the negative (hot cathode). As a consequence, they are accelerated towards the positive (an anode) by the use of a high voltage. Again, these electrons emerge from the anode's hole with a velocity that is relatively uniform. Since there is no voltage between the deflecting plates, the beam of electrons has to follow a straight line. These electrons also experience a vertical force because of the voltage that is connected to the plates. In turn, the vertical force that is constant causes such a beam to follow the path that is parabolic. An increase in the voltage of deflection results in the increase in the curve.

Works Cited

Findlay, R. P. "Induced Electric Fields in The MAXWELL Surface-Based Human Model from Exposure to External Low-Frequency Electric Fields." Radiation Protection Dosimetry, vol. 162, no. 3, 2013, pp. 4-7. Oxford University Press (OUP), doi:10.1093/rpd/nct281.

Kroemer, Herbert. "Quasi-Electric Fields and Band Offsets: Teaching Electrons New Tricks (Nobel Lecture)." Chemphyschem, vol 2, no. 8-9, 2001, pp. 9-11. Wiley-Blackwell, doi:10.1002/1439-7641(20010917)2:8/93.3.co;2-t.

Peter, Laurence. "Cheminform Abstract: “Sticky Electrons” Transport and Interfacial Transfer of Electrons in The Dye-Sensitized Solar Cell." Cheminform, vol. 41, no. 17, 2010, pp. 2-5. Wiley-Blackwell, doi:10.1002/chin.201017270.

April 13, 2023
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