A cathode-ray tube (CRT) is a sealed, evacuated glass tube with a filament at one end and a fluorescent screen at the other end (see Figure 1).
When heated, the filament emits cathode rays that are accelerated by an electric potential, V, toward a barrier having a pinhole. Beyond the barrier are 2 conducting plates, each of length L, that have an electric field, E, between them. (The direction of E can be upward or downward; in Figure 1, it is downward.) Any rays that pass through the pinhole travel through the field and strike the screen, producing a bright spot of visible light.
A group of students performed 3 studies on various CRTs, each of which had a ruler taped to the outer surface of the screen (see Figure 2) to measure a spot’s vertical location, y (in centimeters, cm).
The students obtained a CRT having L = 2.5 cm. They set V to 1.0 kilovolt (kV), varied both the direction and the magnitude (in newtons per coulomb, N/C) of E, and recorded the resulting values of y (see Table 1).
Using the CRT from Study 1, the students set the magnitude of E to 1.0 × 104 N/C, varied V, and recorded the resulting values of y (see Table 2).
The students obtained various CRTs, each having a different L. For each CRT, they set V to 1.0 kV, set the magnitude of E to 1.0 × 104 N/C, and recorded the resulting value of y (see Table 3).
1. Studies 1 and 2 differed in which of the following ways? In Study 1, the students determined how the spot’s location varied with:
2. Suppose that the students had performed a trial in Study 2 in which y was 2.6 cm. The value of V in this trial would most likely have been:
3. Figure 2 could serve as an illustration of the result(s) of which trial(s)?
4. Based on the results of Study 1, in which direction did E most likely point in Study 2, and in which direction did E most likely point in Study 3 ?
Study 2 - Study 3
5. Once a CRT is sealed, it cannot be reopened. However, because both V and E are controlled from the outside, a CRT can be used repeatedly under varying conditions. Based on the descriptions of Studies 1-3, what is the minimum number of different CRTs that the students required to complete the 3 studies?
6. Suppose that the students had performed a trial in which the cathode rays traveled all the way from the filament to the screen in a straight-line path, striking the screen at y = 0 cm. Based on the results of Studies 1 and 2, which of the following statements about V and the magnitude of E in this trial would have been true?
7. In a CRT, E is generated by building up equal and opposite electric charges on the 2 conducting plates. Suppose that cathode rays are negatively charged. If E is directed downward as shown in Figure 1, which conducting plate is more likely the negatively charged plate?
1. The correct answer is C.
According to the passage, in Study 1, the students varied the direction and magnitude of E (the electric field). In Study 2, the students varied V (electric potential).
2. The correct answer is B.
According to Table 2, as V increased, y decreased. When y = 3.2 cm, V = 1.0 kV and when y = 2.1 cm, V = 1.5 kV. It follows that if y = 2.6 cm, then V would have some value between 1.0 kV and 1.5 kV.
3. The correct answer is D.
In Figure 2, the spot was located at approximately +3 cm. According to Tables 1 and 2, the trials with spots in this position were Trial 4 and Trial 8 (both at +3.2 cm).
4. The correct answer is C.
According to Table 1, when E had an upward direction, y was negative; when E had a downward direction, y was positive. Table 2 shows that in Study 2, y was positive, indicating that E had a downward direction. Table 3 shows that in study 3, y was negative, indicating that E had an upward direction.
5. The correct answer is B.
According to the passage, in Studies 1 and 2 only, V and E were varied and therefore one CRT with L = 2.5 cm could be used. In Study 3, L was varied, including one trial with L = 2.5 cm. Because five different L values were tested and because L cannot be varied from outside the tube, five different CRTs must have been used.
6. The correct answer is B.
According to the results of Study 1, as the magnitude of E increased, the farther the spot was from y = 0 cm. According to the results of Study 2, as V increased, y decreased. In order to have y = 0 cm, V should be nonzero and the magnitude of E should be zero.
7. The correct answer is D.
In order to answer this item, the examinee should know that charges of like sign repel each other and charges of opposite sign attract each other. According to Figure 1, the cathode ray is deflected upward (toward the top plate and away from the bottom plate). Because like charges repel one another and because the cathode ray is negatively charged, the bottom plate must be negatively charged.