# ADV PHYS

### Sub-Contents

1-1Electrical forces

1-2Electric and magnetic fields

1-3Characteristics of vector fields

1-4The laws of electromagnetism

1-5What are the fields?

1-6Electromagnetism in science and technology

2-1Understanding physics

2-2Scalar and vector fields—T and h

2-3Derivatives of fields—the gradient

2-4The operator ∇

2-5Operations with ∇

2-6The differential equation of heat flow

2-7Second derivatives of vector fields

2-8Pitfalls

3-1Vector integrals; the line integral of ∇ψ

3-2The flux of a vector field

3-3The flux from a cube; Gauss’ theorem

3-4Heat conduction; the diffusion equation

3-5The circulation of a vector field

3-6The circulation around a square; Stokes’ theorem

3-7Curl-free and divergence-free fields

3-8Summary

4-1Statics

4-2Coulomb’s law; superposition

4-3Electric potential

4-4E = − ∇φ

4-5The flux of E

4-6Gauss’ law; the divergence of E

4-7Field of a sphere of charge

4-8Field lines; equipotential surfaces

5-1Electrostatics is Gauss’ law plus . . .

5-2Equilibrium in an electrostatic field

5-3Equilibrium with conductors

5-4Stability of atoms

5-5The field of a line charge

5-6A sheet of charge; two sheets

5-7A sphere of charge; a spherical shell

5-8Is the field of a point charge exactly 1/r 2?

5-9The fields of a conductor

5-10The field in a cavity of a conductor

6-1Equations of the electrostatic potential

6-2The electric dipole

6-3Remarks on vector equations

6-4The dipole potential as a gradient

6-5The dipole approximation for an arbitrary distribution

6-6The fields of charged conductors

6-7The method of images

6-8A point charge near a conducting plane

6-9A point charge near a conducting sphere

6-10Condensers; parallel plates

6-11High-voltage breakdown

6-12The field-emission microscope

7-1Methods for finding the electrostatic field

7-2Two-dimensional fields; functions of the complex variable

7-3Plasma oscillations

7-4Colloidal particles in an electrolyte

7-5The electrostatic field of a grid

8-1The electrostatic energy of charges. A uniform sphere

8-2The energy of a condenser. Forces on charged conductors

8-3The electrostatic energy of an ionic crystal

8-4Electrostatic energy in nuclei

8-5Energy in the electrostatic field

8-6The energy of a point charge

9-1The electric potential gradient of the atmosphere

9-2Electric currents in the atmosphere

9-3Origin of the atmospheric currents

9-4Thunderstorms

9-5The mechanism of charge separation

9-6Lightning

10-1The dielectric constant

10-2The polarization vector P

10-3Polarization charges

10-4The electrostatic equations with dielectrics

10-5Fields and forces with dielectrics

11-1Molecular dipoles

11-2Electronic polarization

11-3Polar molecules; orientation polarization

11-4Electric fields in cavities of a dielectric

11-5The dielectric constant of liquids; the Clausius-Mossotti equation

11-6Solid dielectrics

11-7Ferroelectricity; BaTiO3

12-1The same equations have the same solutions

12-2The flow of heat; a point source near an infinite plane boundary

12-3The stretched membrane

12-4The diffusion of neutrons; a uniform spherical source in a homogeneous medium

12-5Irrotational fluid flow; the flow past a sphere

12-6Illumination; the uniform lighting of a plane

12-7 The “underlying unity” of nature

13-1The magnetic field

13-2Electric current; the conservation of charge

13-3The magnetic force on a current

13-4The magnetic field of steady currents; Ampère’s law

13-5The magnetic field of a straight wire and of a solenoid; atomic currents

13-6The relativity of magnetic and electric fields

13-7The transformation of currents and charges

13-8Superposition; the right-hand rule

14-1The vector potential

14-2The vector potential of known currents

14-3A straight wire

14-4A long solenoid

14-5The field of a small loop; the magnetic dipole

14-6The vector potential of a circuit

14-7The law of Biot and Savart

15-1The forces on a current loop; energy of a dipole

15-2Mechanical and electrical energies

15-3The energy of steady currents

15-4B versus A

15-5The vector potential and quantum mechanics

15-6What is true for statics is false for dynamics

16-1Motors and generators

16-2Transformers and inductances

16-3Forces on induced currents

16-4Electrical technology

17-1The physics of induction

17-2Exceptions to the “flux rule”

17-3Particle acceleration by an induced electric field; the betatron

17-4A paradox

17-5Alternating-current generator

17-6Mutual inductance

17-7Self-inductance

17-8Inductance and magnetic energy

18-1Maxwell’s equations

18-2How the new term works

18-3All of classical physics

18-4A travelling field

18-5The speed of light

18-6Solving Maxwell’s equations; the potentials and the wave equation

19-1Waves in free space; plane waves

19-2Three-dimensional waves

19-3Scientific imagination

19-4Spherical waves

20-1Light and electromagnetic waves

20-2Spherical waves from a point source

20-3The general solution of Maxwell’s equations

20-4The fields of an oscillating dipole

20-5The potentials of a moving charge; the general solution of Liénard and Wiechert

20-6The potentials for a charge moving with constant velocity; the Lorentz formula