Electromagnetic Interactions1
I.H.Hutchinson
This is the HTML version of the notes split by chapters.
It may not render well in your browser because of font problems.
If you prefer, use the (big) pdf version here.
Contents
1 Maxwell's Equations and Electromagnetic Fields
1.1 Introduction
1.1.1 Maxwell's Equations (1865)
1.1.2 Historical Note
1.1.3 Auxiliary Fields and Electromagnetic Media
1.1.4 Units
1.2 Vector Calculus and Notation
1.2.1 Divergence
1.2.2 Curl
1.2.3 Volume Integration
1.2.4 Surface Integration
1.2.5 Line (Contour) Integration
1.2.6 The Meaning of divergence: ∇.
1.2.7 The Meaning of Curl: ∇∧
1.3 Electrostatics and Gauss' Theorem
1.3.1 Point Charge q
1.3.2 Spherically Symmetric Charge ρ(r)
1.3.3 Arbitrary Charge Distribution
1.3.4 Intuitive Picture
1.3.5 Electric Potential (for static problems [(∂)/(∂t)] → 0)
1.3.6 Potential of a Point Charge [General Potential Solution]
1.3.7 Green Function for the Laplacian
1.3.8 Boundary Conditions
1.3.9 Parallel Plate Capacitor
1.3.10 Charge on an arbitrary conductor
1.3.11 Visualizing Electric Potential and Field
1.3.12 Complex Potential Representation 2-D
1.4 Electric Current in Distributed Media
1.4.1 Steady State Conduction
1.4.2 Conductor Boundary Conditions (Steady Currents)
1.5 Magnetic Potential
1.5.1 ∇.B=0 Necessary
1.5.2 ∇.B=0 Sufficient (outline proof by construction)
1.5.3 General Vector Potential Solution (Magnetostatic)
1.5.4 Cartesian Translational Symmetry (2-d x,y)
1.5.5 Cylindrical Symmetry (Circular Loops with common axis)
1.5.6 General Property of Symmetry Situations: Flux Function
1.6 Electromagnetism and Magnets
1.6.1 Simple Solenoid
1.6.2 Solenoid of Arbitrary Cross-Section
1.6.3 Coil Types
1.6.4 Magnetic Dipole
1.6.5 Revisionist History of Electromagnetic Induction
1.6.6 Inductance
2 Particle Motion in Electric and Magnetic Fields
2.1 Electric Field Alone
2.2 Electrostatic Acceleration and Focussing
2.2.1 Immersion Lens
2.2.2 Alternating Gradient Focussing
2.3 Uniform Magnetic field
2.3.1 Brute force solution:
2.3.2 `Physics' Solution
2.3.3 Relativistic Aside
2.3.4 Momentum Spectrometers
2.3.5 Historical Day Dream (J.J. Thomson 1897)
2.3.6 Practical Spectrometer
2.4 Dynamic Accelerators
2.4.1 Cyclotron
2.4.2 Limitations of Cyclotron Acceleration: Relativity
2.4.3 Synchrotron
2.4.4 Linear Accelerators
2.5 Magnetic Quadrupole Focussing (Alternating Gradient)
2.5.1 Preliminary Mathematics
2.5.2 Multipole Expansion
2.6 Force on distributed current density
2.6.1 Forces on dipoles
2.6.2 Force on an Elementary Magnetic Moment Circuit
2.6.3 Example
2.6.4 Intuition
2.6.5 Angular Momentum
2.6.6 Precession of a Magnetic Dipole (formed from charged particle)
3 Dynamics of the Electromagnetic Fields
3.1 Maxwell Displacement Current
3.2 Field Dynamics, Energy and Momentum
3.2.1 Introduction
3.2.2 Poynting's Theorem: Energy Conservation
3.2.3 Momentum Conservation
3.3 Inductance, Energy, and Magnet Stresses
3.3.1 Relation between energy density and magnetic pressure in a solenoid
3.4 Potentials for Time Varying Fields
3.4.1 General Solutions
3.5 Advanced and Retarded Solutions
4 Radiation By Moving Charges
4.1 Potentials and Fields of a moving point charge
4.2 Potential of a Point Charge in Uniform Motion 2
4.3 Fields of a Generally-Moving Charge
4.4 Radiation from Moving Charges
4.4.1 Near Field and Radiation Terms
4.4.2 Radiation into a Specific Solid-angle
4.4.3 Radiation from Non-relativistic Particles: Dipole Approximation
4.5 Radiation from Relativistic Particles
4.5.1 Acceleration Parallel to v
4.5.2 Acceleration Perpendicular to v
4.5.3 Total Radiated Power
4.6 Scattering of Electromagnetic Radiation
4.6.1 Thomson Scattering
4.6.2 Compton Scattering
5 Atomic Structure and Processes
5.1 Elementary atomic structure
5.2 Atomic processes in electromagnetic interactions
5.3 The Photoelectric Effect
5.4 Electrons and Pair Production
6 Collisions of Charged Particles
6.1 Elastic Collisions
6.1.1 Reference Frames and Collision Angles
6.1.2 Classical Coulomb Collisions
6.2 Inelastic Collisions
6.2.1 Energy transfer to an oscillating particle
6.2.2 Straight-Line Collision
6.2.3 Classical Energy Loss Rate Formula
6.2.4 Quantum effects on close collisions
6.2.5 Values of the Stopping Power
6.2.6 Effects of surrounding particles on distant collisions
6.3 Angular Scattering from Nuclei
6.4 Summary
7 Radiation from Charged Particle Interaction with Matter
7.1 Bremsstrahlung
7.1.1 Radiation in Collisions, Non-relativistic.
7.1.2 Bremsstrahlung from light or heavy particles
7.1.3 Comparison of Bremsstrahlung and Collisional Energy Loss
7.1.4 Spectral Distribution
7.1.5 Bremsstrahlung from Relativistic Electrons
7.1.6 Screening and Total radiative loss
7.1.7 Thick target Bremsstrahlung.
7.2 Cerenkov Radiation
7.2.1 Coupling Strength
7.2.2 Energy Spectrum