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Chapter 16 – Charge and Field
17.1 Linear accelerators
Learning outcomes
 Electric field strength E = F
q
 in a UNIFORM FIELD E = V/d
 Electric potential V = electrical potential energy
charge
 energy transfer to/from charge when it moves through a p.d. is W = q
 the velocity at non-relativistic velocities (v << c) of a charge q when it has moved through a
potential difference V is
v 
2qV
m
 electric field strength = - potential gradientand is given by
E 
dV
dx
 an electric field can be represented by field lines and equipotential surfaces, which are
perpendicular to each other
 the evidence for the discreteness of the charge on an electron (that it comes in multiples of 1.6 x
10-19 C)
Lesson 1: Accelerators, electric field and potential
Objectives:
- you know that there is a field there because there is a force on a charge
- in a uniform field E = V/d
- field lines are parallel in uniform field, equipotentials are at right angles to them
- at points where equipotentials are close together the field is strong
- because field is potential gradient
Starter: animation of CERN – how does it work
Display Material 40O 'The linear accelerator'
Demo 10D 'A flame between charged plates'
Demo 20D 'Using a foil strip to look at uniform electric fields'
Demo 30D 'Exploring potential differences in a uniform field' - optional
Define field, uniform field, field = potential gradient
Dis 10O 'The electric field between parallel plates'
Dis 20O 'Acceleration: gravitational and electrical'
Dis 30O 'Two ways of describing electrical forces'
Warm 10W 'The uniform electric field'
Real life situations… Exp 60E 'Measuring potentials in a uniform field conducting paper'
Dis 50O 'Field lines and equipotential surfaces'
Dis 60O Field strength and potential gradient'
Lesson 2:. Using the uniform field - Millikan
Objectives:
- charged objects (oil drops) can be held still/fall with constant velocity in uniform
field
- So you can measure the charge – as Millikan did
Applet for millikan http://physics.wku.edu/~womble/phys260/millikan.html
Dis 70O 'Millikan's experiment'
Use applet or Data 70D 'Millikan's oil drop experiment' to work out value of e.
Lesson 3 More practice
SAQ 60S 'Using uniform electric fields'
MC 20M 'The uniform electric field and its effect on charges'
Demo 180D 'Electrical breakdown.'
Strong fields make sparks
Homework
SoftAct 70S 'Relating field and potential'
Comp 50C 'Electrical breakdown in a vacuum'
Reading 20T Text to Read 'Atmospheric electricity'
Comp 40C 'Thunder clouds and lightning conductors'
Extension: a) Reading 30T Text to Read 'The ultimate speed' + Dis 80O 'The ultimate speed Bertozzi's demonstration'
16.2 Deflecting Charged Beams
Learning outcomes
 a charge follows a parabolic path in uniform electric field
 the force on a moving charge in a uniform magnetic field, F = qvB
 a charge follows a circular trajectory in a uniform magnetic field, radius r = mv
qB
 F = q1q2
and Ee = q1q2
40r 2
40r
 E= q
and V = q
40r 2
40r
in a central field: use of analogy and symmetry arguments
 graphs of all these equations and show how they relate to one another
 electric and magnetic fields are used in particle accelerators
Lesson 4 Parabolic paths in electric fields
Objectives
- electron beams follow parabolic paths between parallel plates
…in cathode ray tubes, CROs
Dis Material 110O 'Deflection plates in an oscilloscope'
Demo 110D 'Deflecting electron beams in an electric field'
Dis 100O 'How an electric field deflects an electron beam'
SoftAct 130S 'Charged particles between plates'
Work out using the maths – constant acceleration so s = ½ a t2. Work out a value for s using the
set up on the deflection tube and see if you get it right.
Lesson 5: Circular paths in magnetic fields
Objectives
- force on a charged particle in a magnetic field F = BQv
- charges go in circles
-
and this is useful in accelerators, particle detectors, medical equipment and
mass spectrometers
Demo 120D Demonstration 'Deflecting electron beams in a magnetic field'
Warm 80W 'Getting F = q v B' – link to Chapter 15
Dis 120O 'How a magnetic field deflects an electron beam'
Dis 130O 'Force on current: force on moving charge'
SoftAct Activity 140S 'Circular motion in a magnetic field'
Dis 140O 'Measuring the momentum of moving charged particles'
Dis 150O 'Principle of the synchrotron accelerator'
Dis 160O 'Electromagnetic waves generated by accelerating charges'
The use of magnetic fields in accelerators, detectors, scanners and spectrometers.
SAQ Question 90S 'Deflection with electric and magnetic fields'
Lesson 6: Questions to try it out and applications of BQv
Objectives
- know how to apply equations to situations involving deflection in magnetic and
electric field
Starter: applet of use of magnets in mass spectrometer, scanner, and bubble chamber pictures.
Discussion of use of magnetic fields.
http://www.physics.upenn.edu/courses/gladney/mathphys/java/sect5/section5_1.html
http://teachers.web.cern.ch/teachers/archiv/HST2000/teaching/resource/bubble/bubble.htm
SAQ Question 100S 'The cyclotron'
MC 110M 'Charged particles in electric and magnetic fields
SAQ 150S 'Charged particles moving in magnetic fields'
Tracks in bubble chambers, and another look at the cyclotron
Summary poster activity – deflection using F = VQ/d on the left, F = BQv on the right.
Lesson 7: Detecting charges: non-uniform electric fields
Objectives
- fields and potential with spherical geometry.
Revise equations from Chapter 11 – gravitational fields. Charge equations by analogy. F equation
is Coulomb’s Law, like Newton’s Law.
SoftAct 270S 'Radial force, field and potential'
Dis 210O 'Force, field, energy and potential'
Pres 210P 'The 1/r hill: Slope and force'
The hill can be used to demonstrate the equations
Demo 200D 'Exploring potential differences round a charged sphere' - optional
Exp 220E 'Plotting potentials in non-uniform fields''
Exp 230E 'Measuring potential differences between concentric conductors'
E fields are concentrated around points.
Dis 170O 'Shapes of electrical fields'
Dis 180O 'Electrical fields with cylindrical symmetry'
Lesson 8: Coulomb’s Law, e.m. waves and equation practice
Objectives
- know how you test Coulomb’s Law
- be able to use the equations
Question 210D: Data Handling Testing Coulomb’s law
SAQ 180S 'Non-uniform electric fields'
Covers all the ideas in this episode: use of symmetry to complete a field pattern, relationship
between equipotentials and field strength, Coulomb's law, potential in a radial field.
Moving charges in dipoles make electromagnetic waves.
Show applets
http://www.phys.hawaii.edu/~teb/java/ntnujava/emWave/emWave.html
Data 170D 'The electric dipole 'using Excel if time or for homework
Lesson 9: Further practice
Objectives
- be able to use the equations
SAQ 200S 'Using the 1/r 2 and 1/r laws for point charges'
MC 220M 'Relationships for force and field, potential and potential energy'
SAQ 190S Short Answer 'Charged spheres: Force and potential'
Homework
Data 130D 'The proton synchrotron' not Q13 + 14 optional
Reading 40T Text to Read 'Some information about LEP at CERN'
SoftAct 240S 'Mapping inverse square vector fields'
SoftAct 250S 'Summing vector fields'
MCQ 240M 'Fields and charged particles'
Question 260E Estimates 'Estimating with fields'
Extension: a) Data 130D 'The proton synchrotron' Q13 + 14
b) ExExQ 230X 'The inverse square law applied to nuclear phenomena'
c) ExExQ 120X 'Deflection of charged particles in a magnetic field'
d) SAQ 250S 'Controlling charged particles'
e) The Hall Effect (links to magnetism, chemistry etc.) - examples include finding e/m and the mass
spectrometer.
SoftAct 150S ''Velocity filters on a spreadsheet'
Demo 160D 'Measuring the charge to mass ratio for an electron'
SoftAct 170S 'Making a velocity filter'
SAQ 140S 'The Hall effect'
SAQ 160S 'Fields in nature and in particle accelerators'