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Classical Electrodynamics and Theory of Relativity

by @ 10:29 am on December 31, 2007. Filed under Mathematics

File : pdf, 844 KB, 163 pages

CONTENTS
PREFACE

CHAPTER I. ELECTROSTATICS AND MAGNETOSTATICS
1. Basic experimental facts and unit systems
2. Concept of near action
3. Superposition principle
4. Lorentz force and Biot-Savart-Laplace law
5. Current density and the law of charge conservation
6. Electric dipole moment
7. Magnetic moment
8. Integral equations of static electromagnetic field
9. Differential equations of static electromagnetic field

CHAPTER II. CLASSICAL ELECTRODYNAMICS
1. Maxwell equations
2. Density of energy and energy flow for electromagnetic field
3. Vectorial and scalar potentials of electromagnetic field
4. Gauge transformations and Lorentzian gauge
5. Electromagnetic waves
6. Emission of electromagnetic waves

CHAPTER III. SPECIAL THEORY OF RELATIVITY
1. Galileo transformations
2. Lorentz transformations
3. Minkowsky space
4. Kinematics of relative motion
5. Relativistic law of velocity addition
6. World lines and private time
7. Dynamics of material point
8. Four-dimensional form of Maxwell equations
9. Four-dimensional vector-potential
10. The law of charge conservation
11. Note on skew-angular and curvilinear coordinates

CHAPTER IV. LAGRANGIAN FORMALISM IN THEORY OF RELATIVITY
1. Principle of minimal action for particles and fields
2. Motion of particle in electromagnetic field
3. Dynamics of dust matter
4. Action functional for dust matter
5. Equations for electromagnetic field

CHAPTER V. GENERAL THEORY OF RELATIVITY
1. Transition to non-flat metrics and curved Minkowsky space
2. Action for gravitational field. Einstein equation
3. Four-dimensional momentum conservation law for fields
4. Energy-momentum tensor for electromagnetic field
5. Energy-momentum tensor for dust matter
6. Concluding remarks
REFERENCES.

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4 Responses to “Classical Electrodynamics and Theory of Relativity”

  1. This is an excellent find in text on the Internet. (Classical Electrodynamics and Theory of Relativity)

    Thank you for this work and for making it available on the web. Not to mention all of the other items that you have here which are excellent.

    Daniel Jackson
    Project Starlight

  2. Joe Nahhas says:

    Kepler (demolish) Vs Einstein’s

    Ending Einstein’s space jail of time in 2009 that led to fraud Symbol E=mc²

    Areal velocity is constant: r² θ’ =h Kepler’s Law

    h = 2π a b/T; b=a√ (1-ε²); a = mean distance value; ε = eccentricity
    r² θ’= h = S² w’

    S = r exp (ỉ wt); h = [r² Exp (2iwt)] w’=r²θ’
    w’ = (θ’) exp [-2(i wt)]

    w’= (h/r²) [cosine 2(wt) - ỉ sine 2(wt)] = (h/r²) [1- 2sine² (wt) - ỉ sin 2(wt)]
    w’ = w’(x) + ỉ w’(y) ; w’(x) = (h/r²) [ 1- 2sine² (wt)]

    Δ w’= w’(x) – (h/r²) = – 2(h/r²) sine² (wt) = – 2(h/r²) (v/c) ² v/c=sine wt
    (h/ r²)(Perihelion/Periastron)= [2πa.a√ (1-ε²)]/Ta² (1-ε) ²= [2π√ (1-ε²)]/T (1-ε) ²
    Δ w’ = [w'(x) – h/r²] = -4π {[√ (1-ε²)]/T (1-ε) ²} (v/c) ² radian per second

    {x [180/π;degrees]x[100years=36526days;century]x[3600;seconds in degree]
    Δ w” = (-720×36526x3600/T) {[√ (1-ε²]/(1-ε)²} (v/c)² seconds of arc per century

    This Kepler’s Equation solves all the problems Einstein and all physicists could not solve
    DI Her Binary starts systems

    The circumference of an ellipse: 2πa (1 – ε²/4 + 3/16(ε²)²- –.) ≈ 2πa (1-ε²/4); R =a (1-ε²/4) v=√ [G m M / (m + M) a (1-ε²/4)] ≈ √ [GM/a (1-ε²/4)]; m>Exp (ì w t) ———->> S=r Exp (ì wt) Nahhas’ Equation
    Orbit——–>> Orbit light sensing——>> Visual Orbit; Exp = Exponential
    Particle —->> light sensing of moving objects———— >> Wave
    Newton———>>light sensing———->> Quantum
    Quantum = Newton x Visual Effects
    Quantum – Newton = Relativistic = Optical Illusions
    E (Energy by definition) = mv²/2 = mc²/2; if v = c
    m = mass; v= speed; c= light speed; w= angular velocity; t= time
    S = r Exp (ì w t) = r [cos (wt) + ì sin (wt)] Visual effects
    P = visual velocity = change of visual location
    P = d S/d t = v Exp (ì w t) + ì w r Exp (ì w t)
    = (v + ì w r) Exp (ì w t) = v (1 + ì) Exp (ì w t) = visual speed; v = wr
    E (visual energy= what you see in lab) = m p²/2; replace v by p in E = mv²/2
    = m p²/2 = m v²/2 (1 + ì) ² Exp (2ì wt)
    = mv²/2 (2ì) [cosine (2wt) + ì sine (2wt)]
    =ì mv² [1 - 2 sine² (wt) + 2 ì sine (wt) cosine (wt)];v = speed; c = light speed
    wt = π/2
    E (visual) = ìmv² (1 – 2 + 0)
    E (visual) = -ì mc² ≡ mc² (absolute value;-ì = negative complex unit) If v = c
    w t = π/4
    E (visual) = imv² [1-1 +ỉ] =-mc²; v = c
    wt =-π/4+ỉln2/2; 2ỉ wt=-ỉπ/2 – ln2
    Exp (2i wt) = Exp [-ỉπ/2] Exp [ln(1/2)]=[-ỉ (1/2)]
    E (visual) = imv² (-ỉ/2) =1/2mc² v = c
    Conclusion: E = mc² is the visual Illusion of E = mc²/2 joenahhas1958@yahoo.com. All rights reserved.
    PS: In case of E=mc² claims to be rest energy claims then
    E=1/2m (m v + m’ r) ² = (1/2m) (m’ r) ²; v = 0
    E = (1/2m) (mc) ²; m’ r =mc
    E=mc²/2

  3. Joe Nahhas says:

    No Need for relativity

  4. Alexander Nahhas says:

    Einstein’s Physics Dollar Store on Campus
    MIT Harvard Cal-Tech
    Sponsored by NASA
    Why Relativity theory is not Physics and why Einstein’s “thought” = 0
    Walking the walk and talking the talk taking on all space-time confusion of physics by
    MIT Harvard and Cal-Tech and all other Physics dollar stores departments
    And why LHC burned itself

    Visual Effects and the confusions of “Modern” physics

    r ——— Light sensing of moving objects ——- S
    Actual object—– Light ——— Visual object
    r – ——-cosine (wt) + i sine (wt) – S = r [cosine (wt) + i sine (wt)]
    Newton– Kepler’s time visual effects — Time dependent Newton
    Particle ————– Visual effects ——————– Wave

    Line of Sight: r cosine wt

    r ——————- r cosine (wt) line of sight light aberrations

    A moving object with velocity v will be visualized by
    light sensing through an angle (wt);w = constant and t= time
    Also, sine wt = v/c; cosine wt = √ [1-sine² (wt) = √ [1-(v/c) ²]

    A visual object moving with velocity v will be seen as S

    S = r [cosine (wt) + i sine (wt)] = r Exp [i wt]; Exp = Exponential

    S = r [√ [1-(v/c) ²] + ỉ (v/c)] = S x + i S y

    S x = Visual along the line of sight = r [√ [1-(v/c) ²]

    This Equation is special relativity length contraction formula
    And it is just the visual effects caused by light aberrations of a
    moving object along the line of sight.

    In a right angled velocity triangle A B C: Angle A = wt; angle B = 90°; Angle C = 90° -wt
    AB = hypotenuse = c; BC = opposite = v; CA= adjacent = √ [1-(v/c) ²]

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