HOIR?NBỊ2(R2 + z?)z3'1. Starting with the above equation, derive an expression for the magnetic field at the midpoint of theHelmholtz coils.2. Find an expression for the speed of the electrons accelerated through a potential difference Vace-3. Find an expression for the charge to mass ratio, e/m, in terms of v, B, r, by applying Newton's 2ndlaw to an electron in circular motion.4. Combine 2 and 3 to get an expression for e/m in terms of Vace,r, and B. Figure 1: CRT with coils in Helmholtz configuration.The hot cathode emits electrons which are then accelerated through potential difference Vacc. Whenthe electrons enter the magnetic field B, which is perpendicular to their velocity, they move on a circularpath with radius r. The magnetic field is due to coils in Helmholtz configuration (2 coils separateddistance that equals their radius).The magnetic field due to one of the coils with radius R, at a point on the axis distance z away from thecenter of the coil, was found using the Biot-Savart law:HOIR?NB12(R2 + z2)ž

At the center of coil z=0 The equation will reduce to : B = n μoI2R V= W/q q for electron = e W =…

HoIR?N B1 3 2(R2 + z²)7 1. Starting with the above equation, derive an expression for the magnetic field at the midpoint of the Helmholtz coils. 2. Find an expression for the speed of the electrons accelerated through a potential difference Vace: 3. Find an expression for the charge to mass ratio, e/m, in terms of v, B,r, by applying Newton's 2nd law to an electron in circular motion. 4. Combine 2 and 3 to get an expression for e/m in terms of Vacc,r, and B.

HoIR?N B1 3 2(R2 + z²)7 1. Starting with the above equation, derive an expression for the magnetic field at the midpoint of the Helmholtz coils. 2. Find an expression for the speed of the electrons accelerated through a potential difference Vace: 3. Find an expression for the charge to mass ratio, e/m, in terms of v, B,r, by applying Newton's 2nd law to an electron in circular motion. 4. Combine 2 and 3 to get an expression for e/m in terms of Vacc,r, and B.

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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HW #6
Please provide correct answers. Use the following constants if necessary. Coulomb constant, k = 8.987×10^9 N⋅m^2/C^2 . Vacuum permitivity, ϵ0= 8.854×10^−12 F/m. Magnetic Permeability of vacuum, μ0 = 12.566370614356×10^−7 H/m. Magnitude of the Charge of one electron, e = −1.60217662×10^−19 C. Mass of one electron, m_e = 9.10938356×10^−31 kg. Unless specified otherwise, each symbol carries their usual meaning. For example, μC means microcoulomb .