## Classical electrodynamicsThis edition refines and improves the first edition. It treats the present experimental limits on the mass of photon and the status of linear superposition, and introduces many other innovations. |

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Page 533

They must therefore be relations among Lorentz scalars, 4-vectors, 4-

defined by their transformation properties under the Lorentz group in ways

analogous to the familiar specification of

dimensional rotations. We are thus led to consider briefly the mathematical

structure of a space-time whose norm is defined by (11.59). We begin by

summarizing the elements of

The space-time ...

They must therefore be relations among Lorentz scalars, 4-vectors, 4-

**tensors**, etc.defined by their transformation properties under the Lorentz group in ways

analogous to the familiar specification of

**tensors**of a given rank under three-dimensional rotations. We are thus led to consider briefly the mathematical

structure of a space-time whose norm is defined by (11.59). We begin by

summarizing the elements of

**tensor**analysis in a non-Euclidean vector space.The space-time ...

Page 534

A contravariant

according to ? y A convariant

1L64) and the mixed second rank

The generalization to contravariant, covariant, or mixed

should be obvious from these examples. The inner or scalar product of two

vectors is defined as the product of the components of a covariant and a

contravariant vector, B A ...

A contravariant

**tensor**of rank two F°s consists of 16 quantities that transformaccording to ? y A convariant

**tensor**of rank two Gff transforms as , , G'«^lt>G* (1L64) and the mixed second rank

**tensor**Hp° transforms as ^ H'V^H', * (11.65)The generalization to contravariant, covariant, or mixed

**tensors**of arbitrary rankshould be obvious from these examples. The inner or scalar product of two

vectors is defined as the product of the components of a covariant and a

contravariant vector, B A ...

Page 566

(c) For macroscopic media, E, B form the field

What further invariants can be formed? What are their explicit expressions in

terms of the 3-vector fields? 11.13 In a certain reference frame a static, uniform,

electric field Eo is parallel to the x axis, and a static, uniform, magnetic induction

B„ = 2E„ lies in the x-y plane, making an angle 6 with the x axis. Determine the

relative velocity of a reference frame in which the electric and magnetic fields are

parallel.

(c) For macroscopic media, E, B form the field

**tensor**F"" and D, H the**tensor**G"8.What further invariants can be formed? What are their explicit expressions in

terms of the 3-vector fields? 11.13 In a certain reference frame a static, uniform,

electric field Eo is parallel to the x axis, and a static, uniform, magnetic induction

B„ = 2E„ lies in the x-y plane, making an angle 6 with the x axis. Determine the

relative velocity of a reference frame in which the electric and magnetic fields are

parallel.

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### Contents

Introduction and Survey | 1 |

Introduction to Electrostatics | 27 |

BoundaryValue Problems | 54 |

Copyright | |

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### Common terms and phrases

4-vector amplitude angle angular distribution angular momentum aperture approximation assumed atomic axis behavior Bessel functions boundary conditions bremsstrahlung calculation Chapter charge density charge q charged particle classical coefficients collision components conductor consider coordinates cross section current density cylinder defined dielectric constant differential diffraction dimensions dipole direction discussed effects electric and magnetic electric field electromagnetic fields electrons electrostatic energy loss expansion expression factor finite force frequency given Green function incident integral Lagrangian limit linear Lorentz transformation macroscopic magnetic field magnetic induction magnitude Maxwell equations medium modes molecules multipole multipole expansion multipole moments nonrelativistic normal obtain oscillations parallel parameter photon Phys plane wave plasma point charge polarization problem propagation quantum quantum-mechanical radius region relativistic resonant rest frame result scalar scalar potential scattering shown in Fig solution spectrum sphere spherical surface tensor theorem transverse unit vanishes vector potential velocity wave guide wave number wavelength written zero