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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 o to which the electron is accelerated when moving between the electrodes in terms of AV, m, and e. Ov 10 kV X X X 2cm хх e OPI 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. 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.

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 o to which the electron is accelerated when moving between the electrodes in terms of AV, m, and e. Ov 10 kV X X X 2cm хх e OPI 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. 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.

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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I really need help with part A,part B,part C and part D because i don't know how to do the problem is there any chance you can help me and label them 

**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 \( 10^\circ \)? 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 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 \( 10^\circ \) 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: \( B = 2.9 \, \text{mT} \))** **Figure Description:** The figure illustrates a cathode-ray tube setup where an electron moves through a magnetic field. The electron is deflected at an angle \( \theta = 10^\circ \). The field region is \( d = 2.0 \, \text{cm} \) wide, and the trajectory is radial about point \( O \). ***Note:*** This image depicts the essential physics of understanding forces on a charged particle in a magnetic field.
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 \( 10^\circ \)? 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 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 \( 10^\circ \) 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: \( B = 2.9 \, \text{mT} \))** **Figure Description:** The figure illustrates a cathode-ray tube setup where an electron moves through a magnetic field. The electron is deflected at an angle \( \theta = 10^\circ \). The field region is \( d = 2.0 \, \text{cm} \) wide, and the trajectory is radial about point \( O \). ***Note:*** This image depicts the essential physics of understanding forces on a charged particle in a magnetic field.
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