Physics 4BL Lab

Experiment 2: Lorentz Force

Name: Ritvik Agarwal

UID: 404961658

Date Lab Performed: October 18, 2018

Lab Section: Lab 11 (Thursday 2pm – 4:50pm)

TA’s Name: Enrique Jimenez

Lab Partner: Hayato Kato

Worksheet

1. Measurement of e/m

a) When the electron beam is bent into a circle, what is the direction of the magnetic field at the location of the beam?

Using the right-hand rule, with the direction of current, the direction of force and the magnetic field perpendicular to each other, the magnetic field points into the device away from the observer. Following from the magnetic part of the Lorentz force equation

F = -e (v x B)

as the force points towards the center of the circular path of the electrons with a velocity moving in the anticlockwise direction, the cross product of v and B will into the page as the charge is negative for a beam of electrons giving the direction of the magnetic field.

b) Qualitatively, how does the radius of the beam change with accelerating voltage and magnetizing current?

By increasing the accelerating voltage, the radius of the beam increases and vice versa. By increasing the magnetizing current, the radius of the beam decreases and vice versa.

c) Describe the shape of the electron beam trajectories when the magnetic field is not perpendicular to the electron velocity. How does it follow from the Lorentz force equation when the velocity of the electrons have components along the magnetic field and components perpendicular to the field, v = v∥ + v⊥ ?

When the magnetic field is not perpendicular to the electron velocity, the shape of the electron beam trajectory is either a straight beam or a helix.

It is a straight trajectory when the electron velocity is parallel to the magnetic field and therefore there is no force acting on the electron beam as following from the magnetic part of the Lorentz force equation

F = (qv x B)

the cross product of v∥ with B is 0 hence giving a force of 0 N.

It is a helix which propagates in an anticlockwise direction away from the observer when following from the magnetic part of the Lorentz force equation

F = (qv x B)

the electron velocity has a parallel and perpendicular component (v = v∥ + v⊥). The helix is produced as the parallel component will produce a force equal to 0 N and the perpendicular component will produce a force equal to -e (v⊥ x B) which creates the helix.

d) Starting from evB = mv2/R show that if V is the accelerating voltage, e = 2V . m B2R2

2. Diodes

(a) What is the transformer secondary signal compared to voltage rating? Calculate the RMS voltage of this signal (assuming it to be a sine wave) and compare that to the voltage rating.

(b) Record the DC level and the magnitude of the ripple for the full-wave rectifier DC power supply you built.

Presentation Report

### Introduction

The purpose of the experiment is to calculate the charge to mass ratio of an electron which has a value of 1.758820024(11) ×1011 C/kg. We attempt to do this by recreating J.J. Thomson’s experiment using a cathode ray tube and an electron gun. By shooting electrons out of the electron gun in the cathode ray tube, by applying the magnetic part of the Lorentz force equation

F = -e (v x B)

to show that the magnetic field can be used to provide a force that acts towards the center of the circle formed by the electrons being deflected in the anticlockwise direction.

Using the Lorentz force equation when the electron velocity is perpendicular to the magnetic field, we get

evB = mv2/R

For the energy of the system be given by

KE = eV = ½ mv2

we get

e/m = 2V/B2R2

To use the Lorentz force equation, we use Helmholtz coils to provide a uniform, static field to the electrons. The magnetic field is given by

B = 8μ0IN/5√5Rc

where Rc is the radius of the coil where Rc = (0.150 ± 0.005) m and N is the number of turns in the coil where N = 130.00 ± 0.01 turns.

To measure the charge to mass ratio of the electrons, we vary the accelerating voltage and vary the magnetizing current and measure the radius of the circle formed by the electrons. Then we determine the value of e/m using the formula and create a plot of the voltage vs B2R2/2 to obtain e/m as the slope of the regression line.

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