By Professor Dr. Arturo López Dávalos, Professor Dr. Damián Zanette (auth.)
This textbook discusses the basics and purposes of the electromagnetic thought, emphasizing uncomplicated actual facets instead of arithmetic. The textual content is designed for an intermediate point direction, and the subjects are ordered in any such approach as to makes the hyperlinks with a prior path on classical mechanics rather ordinary. additionally, it prepares the reader/student for extra complex classes on quantum mechanics, reliable country physics, box conception, and others. a few particular themes of present curiosity, similar to numerical tools and superconductivity, also are coated. The publication contains a diskette with software program for fixing difficulties in electrostatics and magnetostatics.
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Additional resources for Fundamentals of Electromagnetism: Vacuum Electrodynamics, Media, and Relativity
We notice that, in t his limit, these curves are not longer symmetric, since one of them closes on the x axis while the other opens up. In the new variables, the equation determining the hyperbola that crosses the x axis at x = 1, (x 2 - e2 t2 = 1) is written as x 2 - (elvo)2v6t2 = 1, from which we obtain vot = ± Vo e #=1. Taking the limit e -+ vot = 0 for 00, Ixl 2: 1. this relationship implies 36 2. Relativistic Kinematics In a similar way we can analyze the limit of the equation determining the hyperbola that cuts the vot axis at vot = 1, given by v~t2 - V~X2 /c 2 = 1.
The contravariant four-vectors, denoted by AV (v = 0,1,2,3), transform like the coordinates, A/V = aVJlAJl. 21 ) Four-tensors of rank n are labeled by n indices, and transform as products of n four-vector components. In this case, given a tensor, it is necessary to specify the indices relative to which it is contravariant or covariant. 22) An example of a second rank tensor is the metric tensor 9Jlv' As we show later on, the electromagnetic field is also a tensor of rank two. 4 Covariant Formulation of Mechanics The tensor formulation of relativistic mechanics makes it necessary to redefine the quantities of interest, such as velocity, momentum or force, in terms of tensor entities, so that they have well-defined transformation properties under Lorentz transformations.
This generalization completes the extension of the formalism of classical mechanics to its relativistic covariant version. Given a one-particle system, we postulate the existence of a function £, called the Lagrangian, which is a function of XV and VV, that is to say, of the coordinates and of the velocity. 32) This quantity is defined using the proper time 7 in order to build a covariant formalism. 'ion, we require that both the Lagrangian £ as well as the action 5 are scalars, invariant under Lorentz transformations.