Problems and Solutions in Special Relativity and Electromagnetism

Sergei Kruchinin

• Publisher: WSPC
• Year: 2017
• ISBN:
  9789813227293
• Topic: Physical Sciences
• Subtopic: Astronomy & Astrophysics

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Field theory is an important topic in theoretical physics, which is studied in the physical and physico-mathematical departments of universities. Therefore, lecturers are faced with the urgent task of not only providing students with information about the subject, but also to help them master the material at a deep qualitative level, by presenting the specific features of general approaches to the statement and the solution of problems in theoretical physics. One of the ways to study field theory is the practical one, where the students can deepen their knowledge of the theoretical material and develop problem-solving skills. This book includes a concise theoretical summary of the main branches of field theory and electrodynamics, worked examples, and some problems for the student to solve.

The book is written for students of theoretical and applied physics, and corresponds to the curricula of the theoretical courses "Field theory" and "Electrodynamics" for physics undergraduates. It can also be useful for students of other disciplines, in particular, those in which physics is one of the base subjects.

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--> Contents:

• Foreword
• Introduction
• Vector and Tensor Analyses
• Elements of the Special Theory of Relativity
• Relativistic Mechanics
• Constant Electric and Magnetic Fields in Vacuum
• Electromagnetic Waves
• Field of Moving Charges
• Emission of Electromagnetic Waves

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--> Readership: Teachers and students of theoretical physics at advanced undergraduate level. -->
Electrodynamics;Special Relativity;Field Theory Key Features:

• "Field theory" is an important course from the cycle of subjects of the theoretical physics, which is studied in the physical and physico-mathematical faculties of higher schools
• Each chapter has a brief introduction to the theory, followed by some examples, then problems and finally solutions. Thus the book is "self-contained" in that sense

Section 1

Vector and Tensor Analyses

1.1.Vector and tensor algebras.
Transformation of vectors and tensors

Scalar (invariant) in three-dimensional space is a quantity that is invariant under rotations (inversion) of a coordinate system.

Vector in three-dimensional space is a collection of three quantities that are transformed under rotations of a coordinate system by the formulas

or, according to the rules of tensor analysis,

(where the summation over the repeated indices is assumed). Here,

is the projection of the vector on the α-th axis of the rotated coordinate system; α_αβ is the coefficient of transformation, which is the cosine of the angle between the β-th axis of the initial coordinate system and the α-th axis of the rotated one; A_β is the projection of the vector on the β-th axis of the initial system.

Vectors can be written in terms of contravariant (A^α) or covariant (A_α) coordinates. The square of a three-dimensional vector is the quantity

The scalar product of two vectors defined is as

Second-rank tensor in three-dimensional space is the nine-component quantity T_αβ(α, β = 1, 2, 3), which is transformed under rotations of a coordinate system in the following way:

(as above, the sum over λ and µ is assumed).

Analogously, a third-rank tensor in a three-dimensional space is defined by the law of transformation:

The tensors of higher ranks are defined analogously.

The vector quantities under inversion of a coordinate system can be transformed in two ways. Those vectors, whose components at the inversion of coordinates change sign (transformation x′ = −x,y′ = −y, z′ = −z) are called polar vectors or simply vectors. The vectors, whose components do not change sign under inversion of a coordinate system, are called pseudovectors or axial vectors. (The differ...

Table of contents

• Cover Page
• Title
• Copyright
• Foreword
• Introduction
• Contents
• Section 1. Vector and Tensor Analyses
• Section 2. Elements of the Special Theory of Relativity
• Section 3. Relativistic Mechanics
• Section 4. Constant Electric and Magnetic Fields in Vacuum
• Section 5. Electromagnetic Waves
• Section 6. Field of Moving Charges
• Section 7. Emission of Electromagnetic Waves
• References