Open Proctor

1. The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

0.9%2.4%3.1%4.2%

An electron (mass 𝑚 and charge −𝑒) is placed at point A (Figure 1, 𝑧 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%0.9%0.9%0.9%

An electron is placed at point B (Figure 1, 𝑟 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to harmonic oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%0.9%0.9%0.9%

Determine the focal length 𝑓 of this lens. Assume that 𝑓 ≫ 𝑑. Express your answer in terms of the constant 𝛽 from question B.1 and other known quantities. Assume that before reaching the ”active region” the electron packet is parallel to the 𝑧-axis and 𝑟 ≪ 𝑅. The sign of 𝑞 is such so that the lens is focusing.

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Find 𝑐. Express your answer in terms of the constant 𝛽 from question B.1 andother known quantities.

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Determine the dependence of the charge on the ring as a function of time, 𝑞(𝑡), and make a schematic plot of this dependence. 𝑡 = 0 corresponds to a time moment when electrons are in the plane of the ring. What is the charge on the ring 𝑞0 when the absolute value 𝑞(𝑡) is maximal? The capacitance of the ring is 𝐶 (i.e., you do not have to use the actual expression found in D.1). Remark: the drawn polarity in Figure 3 is for indicative purposes only. The sign should be chosen so that the lens is focusing.

0.9%2.4%3.1%4.2%

Find the focal length 𝑓 of the lens. Assume that 𝑓 /𝑣 ≫ 𝑅0𝐶, but 𝑑/𝑣 and 𝑅0𝐶 are of the same order of magnitude. Express your answer in terms of the constant 𝛽 from part B and other known quantities.

0.9%2.4%3.1%4.2%

1. The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

0.9%2.4%3.1%4.2%

An electron (mass 𝑚 and charge −𝑒) is placed at point A (Figure 1, 𝑧 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%2.4%3.1%4.2%

An electron is placed at point B (Figure 1, 𝑟 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to harmonic oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%2.4%3.1%4.2%

Determine the focal length 𝑓 of this lens. Assume that 𝑓 ≫ 𝑑. Express your answer in terms of the constant 𝛽 from question B.1 and other known quantities. Assume that before reaching the ”active region” the electron packet is parallel to the 𝑧-axis and 𝑟 ≪ 𝑅. The sign of 𝑞 is such so that the lens is focusing.

0.9%2.4%3.1%4.2%

Find 𝑐. Express your answer in terms of the constant 𝛽 from question B.1 andother known quantities.

0.9%2.4%3.1%4.2%

Determine the dependence of the charge on the ring as a function of time, 𝑞(𝑡), and make a schematic plot of this dependence. 𝑡 = 0 corresponds to a time moment when electrons are in the plane of the ring. What is the charge on the ring 𝑞0 when the absolute value 𝑞(𝑡) is maximal? The capacitance of the ring is 𝐶 (i.e., you do not have to use the actual expression found in D.1). Remark: the drawn polarity in Figure 3 is for indicative purposes only. The sign should be chosen so that the lens is focusing.

0.9%2.4%3.1%4.2%

Find the focal length 𝑓 of the lens. Assume that 𝑓 /𝑣 ≫ 𝑅0𝐶, but 𝑑/𝑣 and 𝑅0𝐶 are of the same order of magnitude. Express your answer in terms of the constant 𝛽 from part B and other known quantities.

0.9%2.4%3.1%4.2%

1. The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

0.9%2.4%3.1%4.2%

An electron (mass 𝑚 and charge −𝑒) is placed at point A (Figure 1, 𝑧 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%2.4%3.1%4.2%

An electron is placed at point B (Figure 1, 𝑟 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to harmonic oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%2.4%3.1%4.2%

Determine the focal length 𝑓 of this lens. Assume that 𝑓 ≫ 𝑑. Express your answer in terms of the constant 𝛽 from question B.1 and other known quantities. Assume that before reaching the ”active region” the electron packet is parallel to the 𝑧-axis and 𝑟 ≪ 𝑅. The sign of 𝑞 is such so that the lens is focusing.

0.9%2.4%3.1%4.2%

Find 𝑐. Express your answer in terms of the constant 𝛽 from question B.1 andother known quantities.

0.9%2.4%3.1%4.2%

Determine the dependence of the charge on the ring as a function of time, 𝑞(𝑡), and make a schematic plot of this dependence. 𝑡 = 0 corresponds to a time moment when electrons are in the plane of the ring. What is the charge on the ring 𝑞0 when the absolute value 𝑞(𝑡) is maximal? The capacitance of the ring is 𝐶 (i.e., you do not have to use the actual expression found in D.1). Remark: the drawn polarity in Figure 3 is for indicative purposes only. The sign should be chosen so that the lens is focusing.

0.9%2.4%3.1%4.2%

Find the focal length 𝑓 of the lens. Assume that 𝑓 /𝑣 ≫ 𝑅0𝐶, but 𝑑/𝑣 and 𝑅0𝐶 are of the same order of magnitude. Express your answer in terms of the constant 𝛽 from part B and other known quantities.

0.9%2.4%3.1%4.2%

1. The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

0.9%2.4%3.1%4.2%

An electron (mass 𝑚 and charge −𝑒) is placed at point A (Figure 1, 𝑧 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%2.4%3.1%4.2%

An electron is placed at point B (Figure 1, 𝑟 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to harmonic oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%2.4%3.1%4.2%

1. The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

0.9%2.4%3.1%4.2%

An electron (mass 𝑚 and charge −𝑒) is placed at point A (Figure 1, 𝑧 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%2.4%3.1%4.2%

An electron is placed at point B (Figure 1, 𝑟 ≪ 𝑅). What is the force acting on the electron? Looking at the expression of the force, determine the sign of 𝑞 so that the resulting motion would correspond to harmonic oscillations. The moving electron does not influence the charge distribution on the ring.

0.9%2.4%3.1%4.2%

Determine the focal length 𝑓 of this lens. Assume that 𝑓 ≫ 𝑑. Express your answer in terms of the constant 𝛽 from question B.1 and other known quantities. Assume that before reaching the ”active region” the electron packet is parallel to the 𝑧-axis and 𝑟 ≪ 𝑅. The sign of 𝑞 is such so that the lens is focusing.

0.9%2.4%3.1%4.2%

Find 𝑐. Express your answer in terms of the constant 𝛽 from question B.1 andother known quantities.

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Find 𝑐. Express your answer in terms of the constant 𝛽 from question B.1 andother known quantities.

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3:0:0

Name:

Franklin B. McDaniels

Roll No:

767397348

DOB:

07/16/2002

School No:

89200

Centre No:

87382

Test:

NTC

Test Duration:

3 hours

Test Mode:

Online