PHD
  1. Classical mechanics  1.1. Newtonian mechanics  1.1.1. Laws of motion in Newtonian mechanics  1.1.2. Dynamics of particles and systems  1.1.3. Conservation laws  1.1.4. Central force motion  1.2. Lagrangian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Constraints and normalized coordinates  1.2.4. Noether's theorem  1.3. Hamiltonian mechanics  1.3.1. Hamilton's equations  1.3.2. Canonical conversion  1.3.3. Poisson bracket  1.3.4. Action-angle variable  1.4. Rigid body mobility  1.4.1. Rotation of rigid bodies  1.4.2. Moment of inertia tensor  1.4.3. Euler's equations in rigid body dynamics  1.4.4. Gyroscopic motion  1.5. Chaos and nonlinear dynamics  1.5.1. Stage space and attractive  1.5.2. Bifurcation and chaos theory  1.5.3. Hamiltonian Chaos  1.5.4. Lyapunov exponent
  2. Electrodynamics  2.1. Maxwell's equations  2.1.1. Gauss's law for electricity  2.1.2. Gauss's law for magnetism  2.1.3. Faraday's Law  2.1.4. Ampere's Law  2.1.5. Boundary conditions in Maxwell's equations  2.2. Electromagnetic waves  2.2.1. Wave equation  2.2.2. Polarization  2.2.3. Reflection and Refraction  2.2.4. Waveguides and resonators  2.3. Special relativity  2.3.1. Lorentz transformations  2.3.2. Relativistic energy and momentum  2.3.3. Relativistic electrodynamics  2.3.4. Minkowski spacetime  2.4. Radiation and scattering  2.4.1. Dipole radiation  2.4.2. Multipole expansion  2.4.3. Compton scattering  2.4.4. Thomson and Rayleigh scattering  2.5. Plasma Physics  2.5.1. Debye Screening  2.5.2. Magnetohydrodynamics  2.5.3. Plasma instability  2.5.4. Fusion Plasma
  3. Quantum mechanics  3.1. Foundations of quantum mechanics  3.1.1. Principles of quantum mechanics  3.1.2. Wave function and probability interpretation  3.1.3. Uncertainty principle  3.1.4. Quantum Tunneling  3.2. Schrödinger Equation  3.2.1. Time-dependent Schrödinger equation  3.2.2. Time-independent Schrödinger equation  3.2.3. Eigenvalues and eigenfunctions in the Schrödinger equation  3.2.4. Path integrals in quantum mechanics  3.3. Quantum operators  3.3.1. Commutators and observables  3.3.2. Angular momentum operator  3.3.3. Ladder Operator  3.3.4. Pauli matrices  3.4. Quantum entanglement and measurement  3.4.1. Bell's theorem  3.4.2. Quantum Teleportation  3.4.3. Quantum entanglement and quantum decoherence in measurement  3.4.4. Quantum entanglement and measurement in quantum mechanics  3.5. Relativistic quantum mechanics  3.5.1. Klein–Gordon equation  3.5.2. Dirac equation  3.5.3. Quantum field theory  3.5.4. Feynman path integral
  4. Statistical mechanics and thermodynamics  4.1. Classical thermodynamics  4.1.1. Laws of Thermodynamics  4.1.2. Carnot cycle  4.1.3. Entropy and free energy  4.1.4. Thermodynamic efficiency  4.2. Kinetic theory of gases  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Transport phenomenon  4.2.3. Mean free path  4.2.4. Non-equilibrium systems in the kinetic theory of gases  4.3. Statistical mechanics  4.3.1. Microstates and Macrostates  4.3.2. Partition function  4.3.3. Bose–Einstein and Fermi–Dirac statistics  4.3.4. Fluctuations and correlations  4.4. Phase transition  4.4.1. Important events  4.4.2. Landau theory  4.4.3. Ising model  4.4.4. Renormalization group theory
  5. Quantum field theory  5.1. Second Quantization  5.1.1. Quantum harmonic oscillator in second quantization  5.1.2. Creation and annihilation operators in second quantization  5.1.3. Path Integral in Second Quantization  5.1.4. Fock space  5.2. Quantum Electrodynamics  5.2.1. Feynman diagrams  5.2.2. Renormalization in quantum electrodynamics  5.2.3. Gauge invariance in quantum electrodynamics  5.2.4. Vacuum polarization  5.3. Quantum Chromodynamics  5.3.1. Quarks and gluons  5.3.2. Color range  5.3.3. Lattice QCD  5.3.4. Asymptotic freedom  5.4. Standard model of particle physics  5.4.1. Electroweak theory  5.4.2. Higgs mechanism  5.4.4. Grand Unified Theories
  6. General relativity and gravity  6.1. Einstein's field equations  6.1.1. Ricci tensor and scalar curvature  6.1.2. Schwarzschild solution  6.1.3. Kerr metric  6.1.4. Gravitational waves  6.2. Cosmology  6.2.1. Friedmann equation  6.2.2. Cosmic inflation  6.2.3. Dark matter and dark energy  6.2.4. Large scale structure  6.3. Black holes and wormholes  6.3.1. Event horizon in black holes and wormholes  6.3.2. Hawking radiation  6.3.3. Penrose process  6.3.4. Information paradox in black holes and wormholes
  7. Condensed matter physics  7.1. Crystal structure and lattice  7.1.1. Bravais lattices  7.1.2. Band theory in crystal structure and lattices  7.1.3. Phonons in crystal structure and lattice  7.1.4. Block's theorem  7.2. Superconductivity  7.2.1. BCS principle  7.2.2. Meissner effect  7.2.3. High Temperature Superconductor  7.2.4. Josephson effect

PHD ↓


Electrodynamics


Electrodynamics is a broad field of physics that deals with the study of electromagnetic forces. These are one of the fundamental interactions in nature and are responsible for almost everything around us, including light, electricity, and magnetism. At the core of electrodynamics are Maxwell's equations which provide a comprehensive framework for understanding electric and magnetic fields and their interactions.

Maxwell's equations

Maxwell's equations are a set of four differential equations that describe how electric and magnetic fields interact. These equations integrate the concepts of electricity, magnetism, and optics into a coherent theory. Let's look at these equations one by one:

        1. Gauss's Law: ∇⋅E = ρ/ε₀ - This equation describes how electric charges produce electric fields. "E" is the electric field, "ρ" is the charge density, and "ε₀" is the permittivity of free space.
    
        2. Gauss's Law for Magnetism: ∇⋅B = 0 - This states that there are no 'magnetic charges' or monopoles. "B" represents the magnetic field.
    
        3. Faraday's Law: ∇×E = -∂B/∂t - This law describes how a changing magnetic field can produce an electric field. It's the principle behind electric generators.
    
        4. Ampère's Law with Maxwell's Addition: ∇×B = μ₀(J + ε₀∂E/∂t) - This equation relates magnetic fields to the electric currents that produce them and includes Maxwell's addition of the displacement current.

Electric field

The electric field is a vector field around charged particles. It describes the force exerted on other charged objects within the field. Here is a simplified view of the electric field lines around a positive charge:

The electric field E due to a point charge Q can be calculated using Coulomb's law:

        E = k * |Q| / r²

Here, k is the Coulomb constant, |Q| is the magnitude of the charge, and r is the distance from the charge.

Magnetic field

Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles. A simple example is the field around a bar magnet, shown here:

The magnetic field is usually represented by the symbol B The force on a charge moving in a magnetic field is given by the Lorentz force:

        F = q * (v × B)

Where F is the force, q is the charge, v is the velocity of the charge, and B is the magnetic field.

Electromagnetic waves

A remarkable prediction of Maxwell's equations is that electric and magnetic fields can propagate through space as waves. These are called electromagnetic waves, and they travel at the speed of light. Light itself is an electromagnetic wave.

Consider the following waveform, which shows how the electric and magnetic fields oscillate perpendicular to the direction of wave propagation:

This wave has two components: the electric field oscillates in one plane and the magnetic field in another plane, both perpendicular to the direction of wave travel.

Applications of electrodynamics

Electrodynamics is the backbone of many of the technologies and scientific theories that shape our modern world. Here are some of the major applications:

  • Telecommunication: Electromagnetic waves are the principal carriers of information in various forms of communication such as radio, television, and cellular technology.
  • Electrical power generation: Electrodynamics is fundamental to the operation of alternators and transformers, which are key components of electrical generation and distribution.
  • Medical imaging: Technologies such as magnetic resonance imaging (MRI) rely heavily on the principles of electrodynamics.
  • Industrial Applications: Electric motors, one of the backbones of industry, operate on principles derived from electrodynamics.

Closing thoughts

Electrodynamics provides an incredible insight into our understanding of the universe, unifying diverse phenomena under a single theory. Through its mathematical formulation and the predictive power of Maxwell's equations, we can analyze and understand the dynamic relationship between electric and magnetic fields. This is essential not only for theoretical physics but also for practical applications that revolutionize technology and industry.

As you delve deeper into the concepts of electrodynamics, the complexities can grow, but so does the rewarding experience of understanding how fundamental forces shape the world around us. Exploring beyond the basics in quantum electrodynamics and field theory also shows how integral these principles are to the realm of modern physics.


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Electrodynamics

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