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Problem 2: An electron (mass m, charge -e) in a cathode-ray tube is accelerated through a potential difference of AV = 10 kV, then passes through the d = 2.0 cm wide region of uniform magnetic field shown in Fig.1. What field strength will deflect the electron by 10°? a) Find the expression for the speed u to which the electron is accelerated when moving between the electrodes in terms of AV, m, and e. Ov 10kV X хх e 2cm X X - B √ 10⁰ FIG. 1: The scheme for Problem 2 b) When crossing the region with magnetic field, the electron moves along a circular trajectory of radius r with the center at point O, as shown in Fig.1. Express r in terms of the size of the magnetic field region d and the angle 0. mo c) Using the formula for the radius of the cyclotron orbit, r = mg, and your answers to the previous questions, work out a symbolic formula for B as a function of d, AV, 0, m and e. d) For the electron to be deflected by 10° with respect to its original direction, the angle subtended by the circular part of its trajectory at point O has to be equal to 0 = 10° (make sure that you understand why this is so). Use this and the numerical values of other parameters to compute B. (Answer: B= 2.9 mT.)

Problem 2: An electron (mass m, charge -e) in a cathode-ray tube is accelerated through a potential difference of AV = 10 kV, then passes through the d = 2.0 cm wide region of uniform magnetic field shown in Fig.1. What field strength will deflect the electron by 10°? a) Find the expression for the speed u to which the electron is accelerated when moving between the electrodes in terms of AV, m, and e. Ov 10kV X хх e 2cm X X - B √ 10⁰ FIG. 1: The scheme for Problem 2 b) When crossing the region with magnetic field, the electron moves along a circular trajectory of radius r with the center at point O, as shown in Fig.1. Express r in terms of the size of the magnetic field region d and the angle 0. mo c) Using the formula for the radius of the cyclotron orbit, r = mg, and your answers to the previous questions, work out a symbolic formula for B as a function of d, AV, 0, m and e. d) For the electron to be deflected by 10° with respect to its original direction, the angle subtended by the circular part of its trajectory at point O has to be equal to 0 = 10° (make sure that you understand why this is so). Use this and the numerical values of other parameters to compute B. (Answer: B= 2.9 mT.)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem 2:** An electron (mass \( m \), charge \(-e\)) in a cathode-ray tube is accelerated through a potential difference of \(\Delta V = 10 \text{ kV}\), then passes through the \( d = 2.0 \text{ cm} \) wide region of uniform magnetic field shown in Fig. 1. What field strength will deflect the electron by 10°? a) Find the expression for the speed \( v \) to which the electron is accelerated when moving between the electrodes in terms of \(\Delta V\), \( m \), and \( e \). b) When crossing the region with a magnetic field, the electron moves along a circular trajectory of radius \( r \) with the center at point \( O \), as shown in Fig.1. Express \( r \) in terms of the size of the magnetic field region \( d \) and the angle \(\theta\). c) Using the formula for the radius of the cyclotron orbit, \( r = \frac{mv}{eB} \), and your answers to the previous questions, work out a symbolic formula for \( B \) as a function of \( d \), \(\Delta V\), \(\theta\), \( m \), and \( e \). d) For the electron to be deflected by 10° with respect to its original direction, the angle subtended by the circular part of its trajectory at point \( O \) has to be equal to \(\theta = 10^\circ\) (make sure that you understand why this is so). Use this and the numerical values of other parameters to compute \( B \). (Answer: \( B = 2.9 \text{ mT} \)). **FIG. 1:** The scheme for Problem 2 features a diagram showing an electron moving through an electric potential difference and subsequently entering a region with a magnetic field, indicated with blue arrows and 'X' representing field lines going into the page. The diagram illustrates the circular path and the deflection angle \(\theta = 10^\circ\) from the original direction. The region width is \( d = 2 \text{ cm} \).
Transcribed Image Text:**Problem 2:** An electron (mass \( m \), charge \(-e\)) in a cathode-ray tube is accelerated through a potential difference of \(\Delta V = 10 \text{ kV}\), then passes through the \( d = 2.0 \text{ cm} \) wide region of uniform magnetic field shown in Fig. 1. What field strength will deflect the electron by 10°? a) Find the expression for the speed \( v \) to which the electron is accelerated when moving between the electrodes in terms of \(\Delta V\), \( m \), and \( e \). b) When crossing the region with a magnetic field, the electron moves along a circular trajectory of radius \( r \) with the center at point \( O \), as shown in Fig.1. Express \( r \) in terms of the size of the magnetic field region \( d \) and the angle \(\theta\). c) Using the formula for the radius of the cyclotron orbit, \( r = \frac{mv}{eB} \), and your answers to the previous questions, work out a symbolic formula for \( B \) as a function of \( d \), \(\Delta V\), \(\theta\), \( m \), and \( e \). d) For the electron to be deflected by 10° with respect to its original direction, the angle subtended by the circular part of its trajectory at point \( O \) has to be equal to \(\theta = 10^\circ\) (make sure that you understand why this is so). Use this and the numerical values of other parameters to compute \( B \). (Answer: \( B = 2.9 \text{ mT} \)). **FIG. 1:** The scheme for Problem 2 features a diagram showing an electron moving through an electric potential difference and subsequently entering a region with a magnetic field, indicated with blue arrows and 'X' representing field lines going into the page. The diagram illustrates the circular path and the deflection angle \(\theta = 10^\circ\) from the original direction. The region width is \( d = 2 \text{ cm} \).
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